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Let $X$ be a vector space, equipped with two norms $\|\cdot\|_1$ and $\|\cdot\|_2$ Which are equivalent. What is the easiest way to prove that these two equivalent norms induce same topology? | Note that (1) all norms on finite dimensional vector space are equivalent. And here (2) norms on vector space are equivalent iff they have same topology. Question : How can we prove (2) ? Please recommend reference Thank you in anticipation | I am trying to get an intuitive idea of how the affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right> + Q_1 \left| 1 \right>$, NCT states another Qubit $S$ cannot be designed such that $S$ is equivalent to the state of $Q$. Now the catch is, what does Equivalent mean? It could mean either that: $S = S_0 \left| 0 \right> + S_1 \left| 1 \right>$ such that $S_0 = Q_0, S_1 = Q_1$. Or it could mean that $S = Q$, meaning that if $S$ is observed to be some value ( for example 0) then $Q$ MUST be that same value, and vice versa. So it seems that point 2, occurs anyways in entangled systems (particularly cat-states), so I can eliminate that option and conclude that that No Cloning states, given a qubit $Q$, it's impossible to make another qubit $S$ such that: $S = S_0 \left| 0 \right> + S_1 \left| 1 \right>$ such that $S_0 = Q_0, S_1 = Q_1$. Is this correct? | eng_Latn | 4,000 |
Could there be 3 particles (instead of only 2 particles) that could be connected by same quantum entanglement (like minus, plus and "some third position")? | So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I wonder. (It's hard to think of three particles entangled in spin, or so.) | Im trying to run the following code \documentclass[border=10pt]{standalone} \usepackage{pgfplots} \pgfplotsset{width = 7cm, compat = 1.8} \begin{document} \begin{tikzpicture} \begin{axis}[domain = -2:2, domain y = 0:2*pi] \addplot3[contour gnuplot = {output point meta = rawz, number=10, labels=false}, samples = 41, z filter/.code=\def\pgfmathresult{-1.6}] {exp(-x^2) * sin(deg(y))}; \addplot3[surf, samples = 25] {exp(-x^2) * sin(deg(y))}; \end{axis} \end{tikzpicture} \end{document} and I'm getting the error Package pgfplots Error: sorry, plot file{Utitlled_contourmp0.table} could not be opened through a quick search I found out that contour maps require pgfplots and gnuplot to talk to each other. In theory the way to make them interact is adding !TEX option = --enable-write18 or %!TEX option = --enable-escape at the top of the file. Unfortunately this has not worked for me. Any suggestions? | eng_Latn | 4,001 |
How can i reach the treasure in the right door of Desert Temple? I can't jump there. | It's big and empty and I can't get up to the top, what should I do? I can't jump high enough, anti-gravity doesn't seem to do anything either. My first tactic was to use the octopus summoning crown to create a pile of octopi that I could climb up, but when I teleported to the back of the room they followed me back, trapping me in the entrance. | When constructing the matrices for the two CNOT based on the target and control qubit, I can use reasoning: "If $q_0$==$|0\rangle$, everything simply passes through", resulting in an Identity matrix style $\begin{bmatrix}1&0\\0&1\end{bmatrix}$ in the top left. "If $q_0==|1\rangle$, we need to let $q_0$ pass and swap $q_1$, resulting in a Pauli X $\begin{bmatrix}0&1\\1&0\end{bmatrix}$ in the bottom right. $CNOT \equiv \begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{bmatrix}$ "If $q_1$==$|0\rangle$, everything simply passes through", results in leaving $|00\rangle$ and $|10\rangle$ unaffected. "If $q_1==|1\rangle$, we need to let $q_1$ pass and swap $q_0$, mapping $|01\rangle$ to $|11\rangle$ and $|11\rangle$ to $|01\rangle$ $CNOT \equiv \begin{bmatrix}1&0&0&0\\0&0&0&1\\0&0&1&0\\0&1&0&0\end{bmatrix}$ This all seems to check out, but here comes my question: I would like to know if there is a more mathematical way to express this, just as there would be when combining for instance two hadamard gates: $H \otimes H \equiv \frac{1}{\sqrt{2}}\begin{bmatrix}1&1\\1&-1\\ \end{bmatrix} \otimes \frac{1}{\sqrt{2}}\begin{bmatrix}1&1\\1&-1\\ \end{bmatrix} = \frac{1}{2}\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1 \end{bmatrix}$ And a bonus question: How I can, using notation like "CNOT", show which qubit is the control bit and which qubit the target bit? | eng_Latn | 4,002 |
Quantization of energy A mirror reflects all electromagnetic waves that fall on it in the visible spectrum. How does the mechanism of reflection work? Is it because when a photon hits an electron, the electron jumps to a higher energy level and then to come back to its initial energy level, it emits a photon. If the energy levels of an atom are quantized, how can a mirror absorb all e.m waves in the visible spectrum? Shouldn`t it absorb only specific wavelengths? | Explain reflection laws at the atomic level The "equal angles" law of refection on a flat mirror is a macroscopic phenomenon. To put it in anthropomorphic terms, how do individual photons know the orientation of the mirror so as to bounce off in the correct direction? | How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is $$ H = \left(\begin{array}{cc} E_1 & 0 \\ 0 & E_2 \end{array}\right) \, .$$ This can be recast as $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$ $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system. My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? | eng_Latn | 4,003 |
How are quantum gates implemented in reality? Quantum gates seem to be like black boxes. Although we know what kind of operation they will perform, we don't know if it's actually possible to implement in reality (or, do we?). In classical computers, we use AND, NOT, OR, XOR, NAND, NOR, etc which are mostly implemented using semiconductor devices like diodes and transistors. Are there similar experimental implementations of quantum gates? Is there any "universal gate" in quantum computing (like the NAND gate is universal in classical computing)? | How are quantum gates realised, in terms of the dynamic? When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions. In some sense, these are rather mysterious objects, in that they perform "magic" discrete operations on the states. They are essentially black boxes, whose inner workings are not often dealt with while studying quantum algorithms. However, that is not how quantum mechanics works: states evolve in a continuous fashion following Schrödinger's equation. In other words, when talking about quantum gates and operations, one neglects the dynamic (that is, the Hamiltonian) realising said evolution, which is how the gates are actually implemented in experimental architectures. One method is to decompose the gate in terms of elementary (in a given experimental architecture) ones. Is this the only way? What about such "elementary" gates? How are the dynamics implementing those typically found? | How do I apply differential cryptanalysis to a block cipher? I have read a lot of summaries of block ciphers particularly with regards to the NIST competitions stating that reduced-round block ciphers are – for example – vulnerable to differential cryptanalysis. I have a general idea that the application of differential cryptanalysis is to look at the difference between inputs; makes that fairly clear. However, I could take any two inputs for any given block cipher and I am pretty certain I'd be staring at random differences. I am aware this is the idea of a well written block cipher; however, assuming a broken or vulnerable cipher (feel free to provide simple examples) how do I go about choosing differences to try? Are there any clues in algorithm design that would inform a decision on which values to choose? How does being vulnerable to differential cryptanalysis impact a cipher in the wild? If all I have are differences between known plain-texts and known keys as my analysis and a captured ciphertext as my data to exploit, what can I actually deduce? | eng_Latn | 4,004 |
Confused about the application of Hadamard gate to uncorrelated qubits Why does applying the following circuit on a $00$ state produce $|0\rangle \otimes |+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |01\rangle)$. Shouldn't it produce $ |+\rangle \otimes |0\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |10\rangle)$? | Big Endian vs. Little Endian in Qiskit I've noticed that Q# favors Little Endian. Meaning that most operations are designed for this type of encoding. Is is it the same with Qiskit? | Deriving a QM expectation value for a square of momentum $\langle p^2 \rangle$ I already derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle= \int\limits_{-\infty}^{\infty} \overline{\Psi} \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And I can read clearly that operator for momentum equals $\widehat{p}=- i\hbar\frac{d}{dx}$. Is there an easy way to derive an expectation value for $\langle p^2 \rangle$ and its QM operator $\widehat{p^2}$? | eng_Latn | 4,005 |
Anyone who has studied quantum mechanics know the following relation: $ 2 \otimes 2 = 3 \oplus 1 $ But how did a man woke up and said "Hell yeah, I'll use tensor product of two spin $1/2$ to simulate the interaction of two particles with spin $1/2$" ? Why didn't he start with the direct sum ? (And then, group theory made the magic leading to the relation above) In fact, i'm wondering this because i don't fully understand why we use the tensor product to unite the two Hilbert's space. | My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 that the joint state of two (non-entangled) substates should be the tensor product of the substates: that is, for example, that given a first qubit $$\left|a\right\rangle = \alpha_1\left|0\right\rangle+\alpha_2\left|1\right\rangle$$ and a second qubit $$\left|b\right\rangle = \beta_1\left|0\right\rangle+\beta_2\left|1\right\rangle$$ any non-entangled joint two-qubit state of $\left|a\right\rangle$ and $\left|b\right\rangle$ will be $$\left|a\right\rangle\otimes\left|b\right\rangle = \alpha_1 \beta_1\left|00\right\rangle+\alpha_1\beta_2\left|01\right\rangle+\alpha_2\beta_1\left|10\right\rangle+\alpha_2\beta_2\left|11\right\rangle$$ but it isn't clear to me why this should be the case. It seems to me there is some implicit understanding or interpretation of the coefficients $\alpha_i$ and $\beta_i$ that is used to arrive at this conclusion. It's clear enough why this should be true in a classical case, where the coefficients represent (where normalized, relative) abundance, so that the result follows from simple combinatorics. But what accounts for the assertion that this is true for a quantum system, in which (at least in my text, up to this point) coefficients only have this correspondence by analogy (and a perplexing analogy at that, since they can be complex and negative)? Should it be obvious that independent quantum states are composed by taking the tensor product, or is some additional observation or definition (e.g. of the nature of the coefficients of quantum states) required? 1: (bottom of p. 18) "so the state of the two qubits must be the product" (emphasis added). | It is well know that $SO(n)$ is connected and $O(n)$ has two connected components: $O^+(n)=\{A\in O(n):\det A=+1\}$ and $O^-(n)=\{A\in O(n):\det A=-1\}$. In what book can I find this property? | eng_Latn | 4,006 |
Is this possible to build a quantum network? Since quantum entangled particles can transfer the data of their spin properties faster than the speed of light and without any problem of weak signal, can we use quantum entanglement to transfer phone calls and internet connection? Why are we not building up a telecommunication structure based on this technology? What is stopping us? What are the practical difficulties in this process? | Quantum entanglement faster than speed of light? recently i was watching a on quantum computing where the narrators describes that quantum entanglement information travels faster than light! Is it really possible for anything to move faster than light? Or are the narrators just wrong? Regards, | Shannon confusion and diffusion concept I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that confusion is enforced using substitution. Diffusion is enforced using permutation/transposition. Ciphers must use both of them because either confusion or diffusion alone are not enough. I read that a substitution cipher can apply by itself confusion(only). Permutation/Transposition applies by itself diffusion(only). It's precisely the last case that bothers me: Can a permutation/transposition cipher by itself apply diffusion? Shannon explains diffusion as a property that spreads statistic properties of text all over the text preventing statistic analysis. It's frequently translated to: an alteration to a plaintext symbol affects many cipher text symbols. Assuming permutation of bits or characters, how can diffusion be achieved by simple permutation? I mean, if you permute bits, there will be no other bits affected. But if you consider a symbol a character and you permute bits, a change in a character will affect many other characters. It's a question of what is a symbol. I also read versions of this diffusion concept where the point was just changing bits order just to avoid pattern analysis of the text. But, where is the avalanche effect in simple permutation? So, what is the correct definition and the implications of diffusion? I hope you understand what is troubling me. Thank you once more | eng_Latn | 4,007 |
Bands disappear after Raster Calculation ArcGIS I have a tif file containing 36 bands. After I applied raster calculation on the file the bands aggregate into one single band which I don't want because I need them for further calculation. People say that I can apply raster calculation on each band. I can do that but it is too troublesome .Is there any better way to keep all the bands as well as performing calculations on them? | How to prevent RGB composite flatten to 1 band after raster calculation I have a series of landsat wanting to process in raster calculator, but after doing the tool it happened these output images only contain one single band. They used to be RGB 3-band images. It is on arcmap 10.3. I was using raster calculator to remove a certain value in my 3-band landsat image. After I type in the conditional statement to remove all 0 value from the inpur RGB image, it only returns an image of 1band, black and white. How can I preserve the RGB value in output. | How to find the reduced density matrix of a four-qubit system? I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix of system A. I know I could separately extract qubits 1,2 and 3,4 into their own state vectors then find their density matrices and compute the reduced density matrix for system A. I want to figure out how to do this without having to extract and separate the systems. First I would find the density matrix of $|p\rangle$ and then do a partial trace with respect to system B. I am not sure how to do the partial trace of system B since the system contains 2 qubits. Can anyone help me figure this out? I am using Python and NumPy for reference. | eng_Latn | 4,008 |
Method to derive Matrix description of a circuit | How to interpret a quantum circuit as a matrix? | Direct proof that nilpotent matrix has zero trace | eng_Latn | 4,009 |
How do calculate ? | Is my expansion of the state $| x \rangle$ correct? | What are the answers for these basic quetions? | eng_Latn | 4,010 |
Source code for Hamiltonian measurement in qiskit | How to measure a qubit Hamiltonian in qiskit | Proving a graph has no Hamiltonian cycle | eng_Latn | 4,011 |
What's the point of hyperbolic trigonometric functions? I'm currently learning about hyperbolic trig functions, and i don't really get the point. At first, I found it really weird that the input is the area divided by 2, and just wondered what was the point of it anyways? So, are there any real world applications for this kind of stuff? | Real world uses of hyperbolic trigonometric functions I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples of their uses outside academia? | How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is $$ H = \left(\begin{array}{cc} E_1 & 0 \\ 0 & E_2 \end{array}\right) \, .$$ This can be recast as $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$ $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system. My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? | eng_Latn | 4,012 |
Are sufficiently large key sizes enough to deter quantum attacks for symmetric key ciphers such as AES? | We know speedup brute-force attacks two times faster in block ciphers (e.g brute-forcing 128-bit keys take $2^{64}$ operations, not $2^{128}$). That explains why we are using 256-bit keys to encrypt top secrets. But on AES shows brute-forcing AES-256 take $2^{100}$ operations. Does this attack work with Grover's search to make AES cipher quantum unresistant? | Suppose I want a strong 20-bit blockcipher. In other words, I want a function that takes a key (suppose the key is 128 bits), and implements a permutation from 20 bits to 20 bits. The set of permutations should be close to a randomly-chosen subset of size $2^{128}$ of all $2^{20}!$ permutations on 20 bits. I don't want you to build a new blockcipher from scratch. Instead, assume you have a "strong" blockcipher like AES (128-bit blocksize, 128-bit keysize) and use this to build your 20-bit cipher. Of course, your construction should be practical (i.e., you should be able to run it in both directions with reasonable amounts of time and memory). | eng_Latn | 4,013 |
QThread: Call a signal in the right thread | QThread and QTimer | Qt signaling across threads, one is GUI thread? | eng_Latn | 4,014 |
help remembering book title - multiverses/bladerunner-ish future. "sphere of influence. 2150"? | Story on quantum indeterminacy: protagonist has to “quantum select” a portable computer’s state | A fiber bundle over Euclidean space is trivial. | eng_Latn | 4,015 |
Good explanation of the QQ-plot algorithm? Anyone know a good explanation of the QQ-plot algorithm? , p.2. has the only one I've found and it's a bit unclear to me (particularly the percentiles and quantiles). | Benefits of using QQ-plots over histograms In , Nick Cox wrote: Binning into classes is an ancient method. While histograms can be useful, modern statistical software makes it easy as well as advisable to fit distributions to the raw data. Binning just throws away detail that is crucial in determining which distributions are plausible. The context of this comment suggests using QQ-plots as an alternative means to evaluate the fit. The statement sounds very plausible, but I'd like to know about a reliable reference supporting this statement. Is there some paper which does a more thorough investigation of this fact, beyond a simple “well, this sounds obvious”? Any actual systematic comparisons of results or the likes? I'd also like to see how far this benefit of QQ-plots over histograms can be stretched, to applications other than model fitting. Answers on agree that “a QQ-plot […] just tells you that "something is wrong"”. I am thinking about using them as a tool to identify structure in observed data as compared to a null model and wonder whether there exist any established procedures to use QQ-plots (or their underlying data) to not only detect but also describe non-random structure in the observed data. References which include this direction would therefore be particularly useful. | What would be an informative introduction to quantum computing software? I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc). In the question below they are looking for courses on the subject, which I am also interested in, and do plan on checking those links out for ideas. What I am looking for are simple videos, articles, or even games, that cover basic quantum theory at an introductory level. There are some games I have looked into and played. Hello Quantum! was fun and informative, though on my end there was still a lack of comprehension on how the quantum computer (or anything else "quantum") would actually function and play out. My focus for the educational platform is more directed towards the software side of quantum computing. Is there anything that gives a good introduction to the functions and uses a quantum computer will have? As well as what language would be best to program one? Also, would there be a way to program a quantum computer through a classical computer? And, is there a simple introduction to any of this already existing? | eng_Latn | 4,016 |
How to check if 2 qubits are entangled? I know that 2 qubits are entangled if it is impossible to represent their joint state as a tensor product. But when we are given a joint state, how can we tell if it is possible to represent it as a tensor product? For example, I am asked to tell if the qubits are entangled for each of the following situations: $$\begin{align} \left| 01 \right>\\ \frac 12(\left| 00 \right> + i\left| 01 \right> - i\left| 10 \right> + i\left| 11 \right> )\\ \frac 12(\left| 00 \right> - \left| 11 \right>)\\ \frac 12(\left| 00 \right> + \left| 01 \right> +i\left| 10 \right> + \left| 11 \right> ) \end{align}$$ | How do I show that a two-qubit state is an entangled state? The Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle )$ is an entangled state. But why is that the case? How do I mathematically prove that? | How can I create a new extensible symbol? Given an arbitrary thin vertical symbol, can I create a new math delimiter from it (and if so, how)? Edit: Ideally, I would like to be able to create an extensible symbol, either built out an existing normal symbol, or even made from scratch. Edit 2: I am pretty sure that what I am after is an explanation of how to create a .tfm file for an extensible symbol (which Werner's answer describes the general structure of, but not how to make one). For example, let's say I wanted to use the \dagger () or \wr () symbol as a delimiter, and write expressions like \[\left\ldagger \sum_{n=1}^\infty a_n \right\rdagger\] where the symbol scaled appropriately. Would there be any distinction between declaring a symmetric delimiter (like \vert), as opposed to one that has inherently different "left" and "right" versions like [ and ]? Now, even being unaware of the inner workings of TeX, I imagine that there has to be lots of information in the fonts for how a delimiter is to be scaled in different situations, and if I try to make my own delimiter, this information won't be present. Would I need to get deep into FontForge or equivalent to achieve my custom delimiters, or is there an easier way? | eng_Latn | 4,017 |
Is quantization of energy a purely mathematical result or is there a fundamental reason behind it? I'm new to QM and have some confusions about QM. It seems to be that the quantization of energy is just some result from solving the equation, like the infinite square well problem, the quantum harmonic oscillator. I wonder if there are some fundamental reasons why we get such weird results | Reason for the discreteness arising in quantum mechanics? What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the boundary conditions, and the quanta in harmonic oscillator arise due to the commutation relations of the ladder operators, which give energy eigenvalues differing by a multiple of $\hbar$. But what actually is the reason for the discreteness in quantum theory? Which postulate is responsible for that. I tried going backwards, but for me it somehow seems to come magically out of the mathematics. | How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is $$ H = \left(\begin{array}{cc} E_1 & 0 \\ 0 & E_2 \end{array}\right) \, .$$ This can be recast as $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$ $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system. My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? | eng_Latn | 4,018 |
Are there sites that allow to learn about quantum computing? So, I wanted to learn about quantum computing. What should I learn and where do I start? | What would be an informative introduction to quantum computing software? I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc). In the question below they are looking for courses on the subject, which I am also interested in, and do plan on checking those links out for ideas. What I am looking for are simple videos, articles, or even games, that cover basic quantum theory at an introductory level. There are some games I have looked into and played. Hello Quantum! was fun and informative, though on my end there was still a lack of comprehension on how the quantum computer (or anything else "quantum") would actually function and play out. My focus for the educational platform is more directed towards the software side of quantum computing. Is there anything that gives a good introduction to the functions and uses a quantum computer will have? As well as what language would be best to program one? Also, would there be a way to program a quantum computer through a classical computer? And, is there a simple introduction to any of this already existing? | What is the "continue" keyword and how does it work in Java? I saw this keyword for the first time and I was wondering if someone could explain to me what it does. What is the continue keyword? How does it work? When is it used? | eng_Latn | 4,019 |
Is the interference quantum mechanical superposition the same as entanglement? Are the interference of two wave functions an equivalent way of saying that they are entangled? | Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon? Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) being in several states at once (which could also involve the exchange of quantum information for a particle that is known to be in several locations simultaneously). I was wondering if all of this was nothing more but the exchange of quantum information between different masses, and if this could clear up all the confusion in terms of how quantum systems connect in this field of science. A clear explanation for how both of these quantum phenomena work, and if they really are connected (the exchange of quantum information?) would be much appreciated. | Can I use a one time pad key twice with random plaintext? I understand the basics of OTP: $|\text{key space}| = |\text{plaintext space}|$ implies perfect security, key reuse destroys this. Cryptanalysis on the $N$-Time Pad for $N > 1$ involves finding patterns in the ciphertext; this, however, all seems based on the premise that patterns exist in the plaintext (e.g. English language). My question is: if $m_1$ and $m_2$ are two truly random strings, and they are both encrypted with the same OTP key to yield $c_1$ and $c_2$, is it possible to recover $m_1$ and $m_2$ from $c_1$ and $c_2$? In other words: while "perfect security" (aka perfect indistinguishability) is obviously lost (constructing a distinguisher for two messages is trivial), is the plaintext still safe? | eng_Latn | 4,020 |
In connection to question, I am wondering how to calculate value $\langle \psi|\phi \rangle$ for arbitrary quantum states $|\psi\rangle$ and $|\phi\rangle$. A swap test is able to return only $|\langle \psi|\phi \rangle|^2$ which means that sign of the product is forgotten in case the inner product is real. Moreover, information about real and imaginary parts is lost in case of complex result. Do you know about any more general method how to calculate the inner product than swap test? | I've been searching for a quantum algorithm to compute the the inner product between two $n$-qubit quantum states, namely $\langle\phi|\psi\rangle$, which is in general a complex number. One can get $|\langle\phi|\psi\rangle|^2$ through thte SWAP test for multiple qubits, but this is not really the inner product as the information of the real and imaginary parts are lost. I came across this , which claims that the task can be done by simply using CZ gates. I'm not sure if I am mistaken, but it seems to me that such a circuit works for computational basis states, but not for general quantum states. Could somebody help me confirm if this is actually the case? If the above algorithm doesn't work for general quantum states, what algorithm would you suggest? | Take a sponge ball and compress it. The net force acting on the body is zero and the body isn't displaced. So can we conclude that there is no work done on the ball? | eng_Latn | 4,021 |
Quantum Entanglement - How To Interpret I have thought about quantum entanglement for some time, and I still don't quite understand the reasoning behind the conclusion that entangled particles somehow can communicate their state to each other instantaneously, even though they are separated by a substantial distance (e.g., the communication would happen faster than the speed of light). From what I gather, the assumption is that each entangled particle is in a superposition of all possible states, and that upon observation of one of the particles, it immediately (and randomly?) converges to only one of the permissible states. If the second (entangled) particle is observed, at the same or at a different time, the second particle is observed to have the same state as the first particle. Is this interpretation correct? Based on the first two answers that I have seen, I will add somewhat to my question. Yes, I realize that quantum entanglement seems to violate Einstein's laws, or he wouldn't have called it "spooky action at a distance". And no, I don't want a lesson in tensor calculus as my answer. The jist of my question is: What observational evidence and logic leads physicists to conclude that there is "spooky action at a distance", rather than conclude that the individual particles are somehow correlated with each other? Round 3: There is approximately a 50% probability that I am about to get to the bottom of the answer that I am looking for, but (in the finest quantum tradition), I'm not sure yet. Anyway, here goes. Based on LENGTHY replies here (for those who went to the effort, thanks), and a bit of background research, I wasn't aware that the quantum state of two entangled particles could not be described independently. I'm not sure why this is, but given this "fact", it makes perfect sense that the physicists from several decades ago didn't like the conclusions that they were drawing. Is it correct that the quantum states of two entangled quantum particles cannot be independently specified? Or is this a case where I can specify either one of the particles, but to specify them as entangled I necessarily have to specify both together? Chris Drost - thanks for the clarification. The occasional text that refers to "communication between particles", "spooky action at a distance" (yes, this quote is decades old), etc., now makes a good deal more sense in the context of the mathematical framework that you described. | Does entanglement not immediately contradict the theory of special relativity? Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does? | Elastic collision in two dimensions Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a direction of angle $\theta$ above the line it was moving previously. Particle with mass $m_2$ moves with speed $v_{2f}$ in a direction of angle $\phi$ below the line which particle with mass $m_1$ was moving previously. Using equations for conservation of momentum and kinetic energy, how can we prove these two equations $\frac{v_{1f}}{v_{1i}}=\frac{m_1}{m_1+m_2}[\cos \theta \pm \sqrt{\cos^2 \theta - \frac{m_1^2-m_2^2}{m_1^2}}]$ and $\frac{\tan(\theta +\phi)}{\tan(\phi)}=\frac{m_1+m_2}{m_1-m_2}$ ? EDIT. Here is what I've done: For the first one, set the $xy$ coordinate system so that the positive direction of the $x$ axis points toward the original path of the particle with mass $m_1$. So we have three equations: $m_1v_{1i}=m_1v_{1f}\cos \theta + m_2v_{2f} \cos \phi$ $0=m_1v_{1f}\sin \theta - m_2v_{2f}\sin \phi$ $m_1v_{1i}^2=m_1v_{1f}^2+m_2v_{2f}^2$. From the second one, we get: $v_{2f}=\frac{m_1v_{1f}\sin \theta}{m_2 \sin \phi}$ Plotting this into third equation, we get $v_{1i}^2=v_{1f}^2(1+\frac{m_1 \sin^2 \theta}{m_2 \sin^2 \phi})$ (1) From the first equation, we have $\cos \phi =\frac{m_1(v_{1i}-v_{1f}\cos \theta)}{m_2v_{2f}}$ which after applying the equation we have for $v_2f$ becomes $\sin^2 \phi = \frac{1}{1+\frac{(v_{1i}-v_{1f}\cos \theta)^2}{\sin^2 \theta \times v_1f^2}}$ Plotting this into equation (1), gives us an equation in terms of $m_1$, $m_2$, $v_{1f}$, $v_{1i}$ and $\theta$, but it is too far from what I expected. For the second one, assigning the $xy$ coordinate in a way that the positive direction of the $x$ axis points toward the final path of the particle $m_2$, will give us three equations (two for conservation of linear momentum and one for conservation of kinetic energy), but I don't know what to do next. | eng_Latn | 4,022 |
The Bakery: Advanced Pagination | From The Bakery, there's a new tutorial looking to help make pagination (more than just the basic stuff) simple on your site. This tutorial will attempt to cover some advanced techniques of pagination. In large this will cover Ajax pagination. Hopefully we can also uncover some of the better practices and techniques to use with pagination. They look at four different topics: Ajax Pagination Searching (use of pagination on the results page) Other Techniques some of the Known Weaknesses the method has Code is included. | By Joe Bauman Deseret Morning News A University of Utah physicist and his team have made a breakthrough that could pave the way to quantum computing, in which computers can calculate many billions of times faster than they do now. | eng_Latn | 4,023 |
Transportation using disintegration Is it physically possible to have one device, that will scan one object atom by atom and record it to some computer file and then send it to some other machine that could use this blueprint to rebuild that object? What are limitations of this? | Quantum teleportation - the alternative to destroying atoms Can't you just disassemble, not destroy our atoms and transport them to another teleporter via networking or telecoms? This is my thinking of how to keep the same person, not an exact copy of him/her, alive when teleporting. Please answer to tell me if it's possible or not. | How can I send same email multiple times in iOS? I wanted to send a single email to different users. I save an email to drafts and send the email to a user and it goes to the sent box instead of staying in the drafts box. Is there a way I can send an email repeatedly from the drafts box? | eng_Latn | 4,024 |
What is spooky about the entanglement? If it doesn't allow for transmitting of any information, what was/is "spooky" about it? Is there anything spooky about it at all in the end? | Why is quantum entanglement considered to be an active link between particles? From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other. In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle. Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred? | What is the "rootless" feature in El Capitan, really? I have just learned about the "Rootless" feature in El Capitan, and I am hearing things like "There is no root user", "Nothing can modify /System" and "The world will end because we can't get root". What is the "Rootless" feature of El Capitan at a technical level? What does it actually mean for the user experience and the developer experience? Will sudo -s still work, and, if so, how will the experience of using a shell as root change? | eng_Latn | 4,025 |
Why is the fusion power on the Voyager not enough to keep the replicators in operation? | If replicators allowed humans to stop working, why were replicators shut down in the Voyager? | Proof that the Casimir invariant of a representation commutes with everything | eng_Latn | 4,026 |
Does the recent announcement of information transmission via entanglement really indicate superluminal information transfer? Given that various answers here at Physics assert that information isn't transferred (such as this ), and given recent , does this invalidate our understanding of what's happening? Is information actually translated superluminally? | Quantum teleportation and no-communication theorem According to the Wikipedia article for the : In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. This analogy is imprecise, because quantum entanglement suggests that perhaps a message could have been conveyed; the theorem replies 'no, this is not possible'. According to the Jet Propulsion's recent article on quantum teleportation: they can effect an entangled photon (B) with another photon (A) to change the state of the other entangled photon. Doesn't this contradict what the no-communication theorem states ? | Can a well-timed Twisted Image kill a player using Tree of Redemption? What happens if my opponent activates and I cast with the life-exchange ability on the stack? Looking at the comp rules, these seem most relevant: 701.8a A spell or ability may instruct players to exchange something (for example, life totals or control of two permanents) as part of its resolution. When such a spell or ability resolves, if the entire exchange can’t be completed, no part of the exchange occurs. Example: If a spell attempts to exchange control of two target creatures but one of those creatures is destroyed before the spell resolves, the spell does nothing to the other creature. 112.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability. Note that some abilities cause a source to do something (for example, “Prodigal Sorcerer deals 1 damage to target creature or player”) rather than the ability doing anything directly. In these cases, any activated or triggered ability that references information about the source because the effect needs to be divided checks that information when the ability is put onto the stack. Otherwise, it will check that information when it resolves. In both instances, if the source is no longer in the zone it’s expected to be in at that time, its last known information is used. The source can still perform the action even though it no longer exists. Is the entire exchange ability countered because the Tree is dead by the time it resolves? Or do we use the "last known state" (toughness 0), thereby killing its controller? | eng_Latn | 4,027 |
A biclustering approach for crowd judgment analysis | Learning Whom to Trust with MACE | Time-bin entangled photons from a quantum dot | eng_Latn | 4,028 |
What is the application of quantum physics? | What are some applications of quantum physics? | What are some good projects that I can do if I know only Java? | eng_Latn | 4,029 |
What are quantum numbers and what do they mean? | What are quantum numbers? | How does QR code work? | eng_Latn | 4,030 |
Quantum Key Distribution (QKD) has been partly developed by the UK's National Physical Laboratory .
It delivers data using photons - the smallest possible packets of light .
QKD shares a key between two users that is made completely secure using quantum mechanics .
Secure system enables eavesdroppers to be detected and phone calls or transactions terminated .
Technology could be used to transmit encrypted personal information, such as patient health records or payments . | By . Ellie Zolfagharifard . A ‘quantum leap’ has been made in encryption technology that could help securely transfer sensitive data. The technology - known as Quantum Key Distribution (QKD) – delivers private data using the smallest possible packets of light. Data could include encrypted personal information, such as patient health records between hospitals, or payments between credit card providers and online retailers. The end of cyber snooping? Quantum Key Distribution (QKD) delivers private data using the smallest possible packets of light. It could be used to transmit encrypted payments between credit card providers and online retailers to prevent people's private information falling into the hands of cyber criminals (illustrated) 'Quantum' is defined as the minimum amount of a physical . entity. A photon is a quantum, for example, as it is the smallest . divisible unit of light: a single light particle. Quantum mechanics, also known as quantum physics, describes . the behaviour of small particles, including photons, as well as atoms, ions and . electrons. The behaviour of these particles can seem counter-intuitive . and often goes against the rules of classical physical systems. One of the fundamental principles of quantum systems is that . they can behave like both particles and waves. Light is commonly referred to . as, and treated like, a wave, but it consists of particles: photons. This type of behaviour, known as wave-particle duality, . gives rise to the strange properties that make the prospect of future quantum . technologies exciting in areas such as communication, timing, navigation and . information security and storage. In theory, quantum . computing could allow for huge amounts of data to be processed, which is even . beyond today's supercomputers, as well as entirely new types of computation. ‘Encrypted data is very secure,’ Alastair . Sinclair from the National Physical Laboratory (NPL) told MailOnline. ‘Its main vulnerability comes from people working out or intercepting . the key which allows it to be unencrypted.’ ‘QKD ensures that the key is transmitted securely. First the key is created and then data scientists can encrypt the data to send it from one party to the other.’ QKD shares a key between two users that is made completely secure using quantum mechanics. It provides an additional layer of security over and above standard methods used by banks and credit card companies to send data encryption ‘keys’ across a network. It works because binary data is encoded into the particles of light. The 'phase' – a property of photons – is altered to represent binary data: a 0 or 1. ‘The . transmitter can encode these photons in two different ways – known as . bases - creating four possible combinations,’ said Mr Sinclair. The photons are randomly encoded, creating a random key and sent at precise time intervals to the receiver. Secure: QKD shares a key (illustrated) between two users that is made completely secure using quantum mechanics. It provides an additional layer of security over and above standard methods used by banks and credit card companies to send data encryption 'keys' across a network . The receiver detects the photons as 0s and 1s but not which base. So it randomly chooses which base it will detect and records the values and bases. Once all the information has been received, the receiver tells the transmitter which bases it detected and the transmitter reveals which were right and wrong. The receiver rejects all wrong detection events – leaving just the correct ones. Armed with this information, it can create the key to first encrypt and subsequently decrypt and unlock the data. The technology works because binary data (illustrated) is encoded into the particles of light. The phase - a property of photons - is altered to represent binary data: a 0 or 1. The transmitter encodes these photons in two different ways - known as bases - creating four possible combinations . ‘The system is secure because it enables eavesdroppers on the line to be detected,’ said Mr Sinclair. ‘Any attempt to monitor the data will interfere with the photons, affecting the encoding. If there is interference, the receiver will terminate the process before the key is produced.’ A consortium of companies, including BT, Toshiba and NPL, recently completed the first successful trial of QKD over a live fibre network. The field trial shows quantum encryption of 40 Gb/s of data on a live optical fibre. Although these are just tests, the data could include phone calls, personal email, bank details and health records. The trial, which is supported by the UK’s innovation agency, the Technology Strategy Board, is the first to use a single ‘lit’ fibre – which is fibre to transmit data and the quantum key itself. The use of a single fibre is significant, as both the quantum ‘key’ and the encrypted data can now use the same pathway for the first time. ‘The laws of Quantum Mechanics dictate that eavesdropper wouldn’t be able to detect the key without fundamentally changing it, so anything untoward can be easily detected,’ Andrew Lord, head of optical research at BT told MailOnline. Early days: Although the technology has only been tested so far, it could one day be used for phone calls, personal email, bank details and health records (illustrated) ‘But if they want somebody to un-encrypt that data at the other end, then obviously they have to send the key too.’ ‘That’s what makes QKD a potentially very secure way of transmitting keys.’ The technology can be used to protect any data being carried by an optical communications system. ‘Any organisation could use it to secure their telephony and video links, whilst businesses could use it to transmit commercially sensitive data,’ said Mr Lord . Researchers, however, are reluctant to put a time-scale on when the technology could be available for wider use. ‘This research is helping us to understand that, and it’s very promising,’ said Mr Lord. ‘We have begun to test an advanced prototype with this trial and we’ll be looking at the possibility of further trials in the future.’ A key is created so that data can be encrypted and sent from one party to the other. Then the key to unlock that data is transmitted securely using Quantum Key Distribution (QKD). Binary data is encoded into tiny light particles called photons. The 'phase' – a property of photons – is altered to represent binary data: a 0 or 1. The transmitter can encode these photons in two different ways – known as bases - creating four possible combinations. The photons are randomly encoded to create a random key and sent at precise time intervals to the receiver. The receiver detects the photons. It can detect 0s and 1s but not which base, so it randomly chooses which base it will detect and records the values and bases. Once all the information has been received, the receiver tells the transmitter which bases it detected and the transmitter reveals which were right and wrong. The receiver rejects all wrong detection events – leaving just the correct ones. Armed with this information, it can create the key to first encrypt and subsequently decrypt or unlock the data. The system is secure because it enables eavesdroppers on the line to be detected. Any attempt to monitor the data will interfere with the photons, affecting the encoding. If there is interference, the receiver will terminate the process before the key is produced. Any attempt to monitor or interfere with the transmitted key while it’s being sent will be detectable. | The Seattle Seahawks have revealed that a good part of their defensive strategy at the Super Bowl came from the fact that they were able to decode Peyton Manning's hand signals on the field. Controversial corner back Richard Sherman said that he and his fellow defenders cracked the code that the Denver Broncos quarterback was using, meaning that they knew exactly what to expect for each play. 'We knew what route concepts they liked on different downs, so we jumped all the routes. Then we figured out the hand signals for a few of the route audibles in the first half,' he said. Scroll down for video . Cracking the code: The Seattle defense allegedly figured out what plays were associated with each of Peyton Manning's calls, meaning that they were able to prepare for them precisely each play . Reading the field: Manning reportedly changes his hand signals each game, but Seahawks' corner back Richard Sherman said that they were able to break the code during the first quarter of the Super Bowl . Not change enough: Though he only said 'Omaha' twice during the game, he did stick to his same hand signals throughout, meaning that the Seahawks were able to use their cracked code in all four quarters . If true, that would explain why the Broncos had so much trouble scoring, getting their only points on the board in the third quarter. 'All we did was play situational football,' Sherman told Sports Illustrated's blog The MMQB (The Monday Morning Quarterback). 'Me, Earl (Thomas), Kam (Chancellor)... we’re not just three All-Pro players. We’re three All-Pro minds.' The Stanford-educated football player, . who took criticism and was fined for his self-agrandizing speech . following the NFC Championship playoff game, later described the Super . Bowl as 'playing chess, not checkers'. Victorious: Richard Sherman got hurt during the game, but that didn't stop him from celebrating afterwards . New title: The Super Bowl loss means that Manning has taken over the title of 'most post season losses by a quarterback' which was previously held by Brett Favre . Manning's hand signals are known . within the league for being one of his common traits on the field, just . as the call 'Omaha' is associated with the 37-year-old. Manning . is so closely associated with 'Omaha' that 15 companies pledged to . donate $1,500 to charity each time that he said it during the Super . Bowl. Instead of his typical double digit mentions, he only said it twice during Sunday night's big game. (By comparison, Fox Sports reported that he said it 31 times during the AFC title game.) In . post game interviews, however, Manning and other Broncos offensive . linemen explained that the noise at MetLife stadium stopped some of . their verbal messages to one another. Hero's welcome: The Seahawks arrived back Monday ahead of the Wednesday parade in their honor . Home ground: Sherman, who is now on crutches, and the team arrived back in Seattle Monday morning . 'None of us heard the snap count,' Denver offensive lineman Manny Ramirez said. 'I thought I did and when I snapped it, I guess Peyton was actually trying to walk up to me at the time. I'm not 100 per cent sure. It's unfortunate things didn't go as planned.' As for the hand signals, Manning is said to change them every game but this time the other team was paying very close attention early on, explaining how they were able to thwart his plans in the first quarter. The other problem that plagued Manning was that he didn't switch up the system after realizing that it wasn't working. 'Now, if Peyton had thrown in some double moves, if he had gone out of character, we could’ve been exposed,' Sherman said. | eng_Latn | 4,031 |
Physicists create new form of matter that may hold the key to developing quantum machines | Harvard physicists have created a new form of matter -- dubbed a time crystal -- which could offer important insights into the mysterious behavior of quantum systems.
Traditionally speaking, crystals -- like salt, sugar or even diamonds -- are simply periodic arrangements of atoms in a three-dimensional lattice.
Time crystals, on the other hand, take that notion of periodically-arranged atoms and add a fourth dimension, suggesting that -- under certain conditions -- the atoms that some materials can exhibit periodic structure across time.
Led by Professors of Physics Mikhail Lukin and Eugene Demler, a team consisting of post-doctoral fellows Renate Landig and Georg Kucsko, Junior Fellow Vedika Khemani, and Physics Department graduate students Soonwon Choi, Joonhee Choi and Hengyun Zhou built a quantum system using a small piece of diamond embedded with millions of atomic-scale impurities known as nitrogen-vacancy (NV) centers. They then used microwave pulses to "kick" the system out of equilibrium, causing the NV center's spins to flip at precisely-timed intervals -- one of the key markers of a time crystal. The work is described in a paper published in Nature in March.
Other co-authors of the study are Junichi Isoya, Shinobu Onoda,and Hitoshi Sumiya from University of Tsukuba, Takasaki Advanced Research Institute and Sumitomo, Fedor Jelezko from University of Ulm, Curt von Keyserlingk from Princeton University and Norman Y. Yao from UC Berkeley.
But the creation of a time crystal isn't significant merely because it proves the previously-only-theoretical materials can exist, Lukin said, but because they offer physicists a tantalizing window into the behavior of such out-of-equilibrium systems.
"There is now broad, ongoing work to understand the physics of non-equilibrium quantum systems," Lukin said. "This is an area that is of interest for many quantum technologies, because a quantum computer is basically a quantum system that's far away from equilibrium. It's very much at the frontier of research...and we are really just scratching the surface."
But while understanding such non-equlibrium systems could help lead researchers down the path to quantum computing, the technology behind time crystals may also have more near-term applications as well.
"One specific area where we think this might be useful, and this was one of our original motivations for this work, is in precision measurement," Lukin said. "It turns out, if you are trying to build...for example, a magnetic field sensor, you can use NV-center spins," he said. "So it's possible these non-equilibrium states of matter which we create may turn out to be useful."
The notion that such systems could be built at all, however, initially seemed unlikely. In fact several researchers (names are Patrick Bruno, Haruki Watanabe, Masaki Oshikawa) went so far as to prove that it would be impossible to create a time crystal in a quantum system that was at equilibrium.
"Most things around us are in equilibrium," Lukin explained. "That means if you have a hot body and a cold body, if you bring them together, their temperature will equalize. But not all systems are like that."
One of the most common examples of a material that is out of equilibrium, he said, is something many people wear on a daily basis -- diamond.
A crystallized form of carbon that forms under intense heat and pressure, diamond is unusual because it is meta-stable, meaning that once it adopts that crystal formation, it will stay that way, even after the heat and pressure are removed.
It is only very recently, Lukin said, that researchers began to realize that non-equilibrium systems -- particularly those known as "driven" systems, which researchers can "kick" with periodic energy pulses, can exhibit the characteristics of a time crystal.
One of those characteristics, he said, is that the crystal's response across time will remain robust with respect to perturbations.
"A solid crystal is rigid...so if you push on it, maybe the distance between atoms changes a little, but the crystal itself survives," he said. "The idea of a time crystal is to have that type of order in a time domain, but it must be robust."
One other important ingredient is typically if you keep pushing a system away from equilibrium it starts heating up, but it turns out there is a class of systems which are resistant to this heating," Lukin added. "It turns out the time crystal effect is strongly related to this idea that a system is excited, but it not absorbing energy."
To build such a system, Lukin and colleagues began with a small piece of diamond which was embedded with so many NV centers it appeared black.
"We subject that diamond to microwave pulses, which change the orientation of the spins of the NV centers," Lukin explained. "That basically takes all the spins that are pointed up and turns them down, and a next pulse turns them back up."
To test the robustness of the system, Lukin and colleagues varied the timing of the pulses to see whether the material would continue to respond like a time crystal.
"If you don't orient all the spins fully up or down each time, then very rapidly, you will end up with a completely random system ," Lukin said. "But the interactions between the NV centers stabilize the response: they force the system to respond in a periodic, time crystalline manner."
Such systems could ultimately be critical in the development of useful quantum computers and quantum sensors, Lukin said, because they demonstrate that two critical components -- long quantum memory times and a very high density of quantum bits -- arent' mutually exclusive.
"For many applications you want both of those," Lukin said. "But these two requirements are usually contradictory....this is a well-known problem. The present work shows that we can achieve the desired combination. There is still a lot of work to be done, but we believe these effects might enable us to create a new generation of quantum sensors, and could possibly in the long run have other applications to things like atomic clocks." | Product News
Quadtech – “Seven colour management breakthroughs”
QuadTech talked to the editorial team of NarrowWebTech explaining how label printers and converters could meet the requirements regarding colour management. In this respect Craig du Mez, brand manager at QuadTech, named seven colour management breakthroughs.
Pre-laminate/Post-laminate colour support ColourTrack press-side recipe correction module Ink strength/anilox colour correction Spot colour tone value calculation to ISO 20654 Enhanced colour measurement through strip scanning Simplified ink quantity tracking via patented “Virtual Scales” Complete, simplified workflow
In addition to rising brand owner demands, printers are faced with an increased pace and complexity of required technological innovation at a time when profit margins are very tight. Add to that increasing requirements to meet new industry standards, an aging workforce, and the scarcity of true colour experts… and the challenges can be extremely daunting.
You want to read the full article from Craig Du Mez about colour management for label printer and converter? Click here! | eng_Latn | 4,032 |
Could quantum computers in the future access parallel realities? | In what ways could quantum computers access parallel realities in the future? | How can self-awareness theoretically affect an artificial intelligence in the real-world? | eng_Latn | 4,033 |
How far away is the Quantum Internet from becoming a reality? | Quantum Computation: How far away is the Quantum Internet from becoming a reality? | When will time travelling (or at least time shifted vision) finally be possible? | eng_Latn | 4,034 |
What should everybody know about quantum spin liquids? | What is a quantum spin liquid? | What are the details behind the creation of the loading "Q" animation? | eng_Latn | 4,035 |
What is the difference of logic in quantum theory? | In a famous paper of 1936 with Garrett Birkhoff, the first work ever to introduce quantum logics, von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic structure for quantum logics. The concept of creating a propositional calculus for quantum logic was first outlined in a short section in von Neumann's 1932 work, but in 1936, the need for the new propositional calculus was demonstrated through several proofs. For example, photons cannot pass through two successive filters that are polarized perpendicularly (e.g., one horizontally and the other vertically), and therefore, a fortiori, it cannot pass if a third filter polarized diagonally is added to the other two, either before or after them in the succession, but if the third filter is added in between the other two, the photons will, indeed, pass through. This experimental fact is translatable into logic as the non-commutativity of conjunction . It was also demonstrated that the laws of distribution of classical logic, and , are not valid for quantum theory. | Compass-M1 transmits in 3 bands: E2, E5B, and E6. In each frequency band two coherent sub-signals have been detected with a phase shift of 90 degrees (in quadrature). These signal components are further referred to as "I" and "Q". The "I" components have shorter codes and are likely to be intended for the open service. The "Q" components have much longer codes, are more interference resistive, and are probably intended for the restricted service. IQ modulation has been the method in both wired and wireless digital modulation since morsetting carrier signal 100 years ago. | eng_Latn | 4,036 |
What is one of the independent multiphase winding sets configured for? | Doubly fed electric motors have two independent multiphase winding sets, which contribute active (i.e., working) power to the energy conversion process, with at least one of the winding sets electronically controlled for variable speed operation. Two independent multiphase winding sets (i.e., dual armature) are the maximum provided in a single package without topology duplication. Doubly-fed electric motors are machines with an effective constant torque speed range that is twice synchronous speed for a given frequency of excitation. This is twice the constant torque speed range as singly-fed electric machines, which have only one active winding set. | The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g., x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which , while . | eng_Latn | 4,037 |
They're obviously not opposed to messing with other races but do they place limits on their interference and/or interactions? We have witnessed Q (John de Lancie) change or alter many things for his amusement, but he only goes so far and usually puts things back as they were when he gets bored or done with whatever he's up to. I have never seen them 'advance' a civilisation, though Q has saved one or two. Do they have a rule for this? | Are there any rulesets or laws for Q or Q continuum? Anything, that would prevent them from doing... anything? Or at least limit them from doing something really bad? In "" episode Q explains to that they can do, have, get, become anything they want or appear anywhere they want, with just a snap of fingers. If that is true and if there are absolutely no borders or limits, they can't pass, then how can universe work in general? Or, how did it manage to exist so far? I mean -- any Q could wipe out Borg, entire human population or even entire universe... with just a snap of fingers. What could prevent Q from doing that? | A scene I made is not rendering, at all. This grey screen stays the same and nothing changes. Here are my settings: [ | eng_Latn | 4,038 |
My understanding of quantum entanglement is that when you measure the state of an entangled particle, its counterpart will measure a correlated state, i.e. we know for sure that if for example Particle A is measured to be in state A, then particle B will definitely be measured to be in a correlated state B at the same instance. So my question is, can we not exploit this property for communication? The way this could be done is that we fix two frequences, say 10 times/second and 20 times/second. At the destination, we always measure 20 times/sec, at the source we measure 10 times/second or 20 times/second depending on whether we want to transmit a 0 or a 1. Then at the destination, based on the measured probability of states, we can decide whether the source was transmitting a 0 or a 1. Would this work? | From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other. In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle. Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred? | I want to make it so I always have 50 entities in an area. So when 1 dies/despawns/leaves the area I want it to detect that and summon in a new entity, and yes I do want them to die/despawn/leave the area so preventing those things is not an option. | eng_Latn | 4,039 |
If I throw only one photon at the slits in Young's double slit experiment, can I get the interface pattern? | If just a single photon hit a single slit interferometer, what would happen? Would you just see a dot on the screen, or would there be a diffraction pattern? Furthermore, if you had a double slit interferometer but also had which-path information would there still be a diffraction pattern even though there is no interference? | I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse the wave function on the other side, such that interference effects would disappear? Making measurements on "bunches" of entangled particles would thus allow FTL communication, by making observed interference effects appear or disappear. How does such an experiment not: 1) Clearly imply that faster-than-light communication is possible? or 2) (if #1 is rejected) Imply that measurement of one half of an entangled pair does not cause the collapse of the other half's wave function. Why doesn't this thought experiment clearly show that if we maintain that FTL communication is ruled out, we must also rule out "universal collapse" in the Copenhagen interpretation? EDIT: Here is an example of an explicit experiment (though I think experts could come up with something better): You can entangle a photon with an electron such that the angle of the photon is correlated with the electron's position at each slit of a double slit experiment. If the photon is detected (it's outgoing angle measured), then which-path information is known, and there is no interference. If the photon is not detected, the interference remains. The experiment is designed such that the photon and electron go in roughly opposite directions, apart from the tiny deflection which gives which-path information. You set up a series of photon detectors 100 ly away on one side, and your double slit experiment 100 ly away in the opposite direction. Now you produce the entangled pairs in bunches, say of 100 entangled pairs, each coming every millisecond, with a muon coming between each bunch to serve as a separator. Then the idea is that someone at the photon detector side can send information to someone watching the double-slit experiment, by selectively detecting all of the photons in some bunches, but not in others. If all of the photons are detected for one bunch, then the corresponding electron bunch 200 ly away should show no interference effects. If all of the photons are not detected for one bunch, then the corresponding electron bunch 200 ly away would show the usual double-slit interference effects (say on a phosphorus screen). (Note that this does not require combining information from the photon-detector-side with the electron-double-slit side in order to get the interference effects. The interference effects would visibly show up as the electron blips populate the phosphorus screen, as is usual in a double-slit experiment when which-path information is not measured.) In such a way the person at the photon detectors can send '1's and '0's depending on whether they measure the photons in a given bunch. Suppose they send 'SOS' in Morse code. This requires 9 bunches, and so this will take 900 milliseconds, which is less than 200 years. The point is that such an experiment would only work if you assume that the measurement of the photon really does collapse the wave function nonlocally. | eng_Latn | 4,040 |
A single photon, passing through a beamsplitter (BS), ends up in the state $\frac{1}{\sqrt2}(a_1^\dagger + a_2^\dagger)\lvert\operatorname{vac}\rangle$, which is a coherent superposition of the two possible spatial modes. Let us consider its momentum. When the photon goes straight its momentum doesn't change. However, when the photon gets deflected, some amount of momentum must have been transferred to the BS, which therefore acquires some (small) amount of momentum in the opposite direction of the photon (see image below). This new tiny momentum will correspond to some phononic excitation of the BS crystalline structure, or something like that. Because the photon ends up in a superposition of the two output modes, the complete output state must be something of the form: $$ \frac{1}{\sqrt2} \Big(\lvert\text{photon up}\rangle\lvert\text{BS steady}\rangle+\lvert\text{photon right}\rangle\lvert\text{BS momentum changed}\rangle \Big).$$ However, we do not care about the final state of the BS, so that the final state of the photon will be obtained by partial tracing over the BS degree of freedom. And here comes the catch: a naive calculation would now lead to the conclusion that, after partial tracing, the final state of the photon is $$ \frac{1}{2} \Big( \lvert\text{photon up}\rangle\langle\text{photon up}\rvert + \lvert\text{photon right}\rangle\langle\text{photon right}\rvert \Big). $$ This is a completely mixed state, which means that the photon is not in a coherent superposition of the output modes. Now, we know very well that this is not actually the case, as the fact that the photon does end up in a coherent superposition is easily tested and well enstablished. So what did we get wrong? The only logical conclusion (that I can see) is that $\lvert\text{BS steady}\rangle$ and $\lvert\text{BS momentum changed}\rangle$ are not orthogonal states, so that partial tracing does not lead to a totally mixed state for the photon. So here comes the question: why are the two final states of the BS not orthogonal? Is there a clean way to see this? Moreover, given that these two states are also necessarily not the same, this means that partial tracing will always lead to some small amount of mixedness in the final photon state. Does this mean that there is a fundamental limit in the purity of the final photon state? | In many experiments in quantum mechanics, a single photon is sent to a mirror which it passes through or bounces off with 50% probability, then the same for some more similar mirrors, and at the end we get interference between the various paths. This is fairly easy to observe in the laboratory. The interference means there is no which-path information stored anywhere in the mirrors. The mirrors are made of 10^20-something atoms, they aren't necessarily ultra-pure crystals, and they're at room temperature. Nonetheless, they act on the photons as very simple unitary operators. Why is it that the mirrors retain no or very little trace of the photon's path, so that very little decoherence occurs? In general, how do I look at a physical situation and predict when there will be enough noisy interaction with the environment for a quantum state to decohere? | The entire site is blank right now. The header and footer are shown, but no questions. | eng_Latn | 4,041 |
In the , photons reach D0 and shows a pattern, before its quantum entangled counterparts reach one of D1, D2, D3, or D4. The pattern differs based on what happens at the beam splitters (BSa and BSb) and whether the which-path information is lost. What if, instead of installing beam splitters BSa and BSb, we install either pure glass panels or pure silver mirrors. Now imagine we place the splitter part of the setup light-years away from earth, with an astronaut who can decide if she wants to put 2 mirrors or 2 glass panels at BSa and BSb. By shooting photons and observing the patterns on D0 on earth, we could instantly tell which decision the astronaut has made. She can then expand this further, encode any information into bits, and achieve FTL communication. It will be something like: we keep shooting photons at D0 and keep seeing interference pattern, until one day we go, "yep, it starts to look like a diffraction pattern now, she must have switched the panels moments ago!" Since no information can travel FTL, I'm sure my idea is flawed, but what's wrong with it? | The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice). Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector. If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't. Alice and Bob can be spatially separated... What am I misunderstanding? The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol... There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: | I think that is pretty good prima-facia evidence that is just facilitating the deposition of crap. | eng_Latn | 4,042 |
I saw that particles can be paired and that no matter the distance what one does so does the other. Now, can we put each particle into a magnetic field where we could manipulate the spin? If you make the particle spin up zero or down for one and the other field detects the spin change you could have an instant communication device for probes and astronauts. | According to the special theory of relativity, distant simultaneity depends on the observer's reference frame. And, according to the quantum theory, in the case of two entangled particles, a measure on one of the particles simultaneously affects the second one. Under which reference frame is this simultaneous? | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 4,043 |
I already know how the Sun uses quantum tunneling to create nuclear fusion, but can't apply it to enzymes. Also, since I'm only in eighth grade, please use relatively simple language. Thanks! | The hydrogen protons undergo quantum tunnelling in the the sun to fuse into helium, but are only able to do so as they are under immense heat and pressure and the protons and electrons get separated. But our digestive system also makes use of quantum tunnelling to quicken the digestive process, but how do the enzymes free up the electrons when our body temperature is so low? | I have heard a few times that one way of describing quantum computers is that they essentially use the computing power of their counterparts in alternate realities that they access through superposition. My first question is, of course, is this actually an accurate description of how quantum computers work, or just a misrepresentation? Also, if it were to be assumed true and taken literally, then presumably all the possible outcomes of any given computation done would be experienced by each of these alternate realities. I have a few questions regarding the implications of this: Would it be correct to say that our universe essentially "spawns" these alternate realities to use for each computation, or that they all exist simultaneously in a higher dimension and only come into contact via the initiation of superposition by each computer at the same time? Would it be possible to create contact between universes via this connection? I'd expect that, if it was, it would be entirely random, and so not only would not cause any information transfer, it also would be completely undetectable, because the deviations would be within the expected probabilities of error rates - but is there any way to circumvent this? | eng_Latn | 4,044 |
Recent news from Yale... We can predict the quantum leap before the particle collapses its superposition. We can even change it to whichever position we like in real time. In layman terms, as I understand with my limited knowledge, Schrodinger's cat can be SAVED. But... Also to my limited knowledge, the core of how a quantum computer works is because of its superposition feature and its uncertainty. Then put these two paragraphs together... If the superposition is now old news, so would quantum computers. Right? What am I missing here? | new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are and . I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding. The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work? | I have heard a few times that one way of describing quantum computers is that they essentially use the computing power of their counterparts in alternate realities that they access through superposition. My first question is, of course, is this actually an accurate description of how quantum computers work, or just a misrepresentation? Also, if it were to be assumed true and taken literally, then presumably all the possible outcomes of any given computation done would be experienced by each of these alternate realities. I have a few questions regarding the implications of this: Would it be correct to say that our universe essentially "spawns" these alternate realities to use for each computation, or that they all exist simultaneously in a higher dimension and only come into contact via the initiation of superposition by each computer at the same time? Would it be possible to create contact between universes via this connection? I'd expect that, if it was, it would be entirely random, and so not only would not cause any information transfer, it also would be completely undetectable, because the deviations would be within the expected probabilities of error rates - but is there any way to circumvent this? | eng_Latn | 4,045 |
When we perform a double slit experiment we receive interference pattern. when we measure in a specific slit the exact location of the photon (or electron) the interference pattern disappears and we receive only 2 light spots with no interference pattern. Now let's assume that we perform the double slit experiment on two entangled photon (or electrons) far away from each other (Alice & Bob). If Alice measures the location of the photon in the slits, she doesn't receive interference pattern, but because of entanglement the location of Bob's photon is now known and he also doesn't get an interference pattern. This way he knows instantaneously that Alice performed a measurement even when she is far away. If she doesn't measure the location of the photon in the slits, they will both receive interference pattern and Bob will know instantaneously that she didn't measure the photons location. This ideas based on the EPR famous paper enables faster than light communication. What did I miss here? | I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse the wave function on the other side, such that interference effects would disappear? Making measurements on "bunches" of entangled particles would thus allow FTL communication, by making observed interference effects appear or disappear. How does such an experiment not: 1) Clearly imply that faster-than-light communication is possible? or 2) (if #1 is rejected) Imply that measurement of one half of an entangled pair does not cause the collapse of the other half's wave function. Why doesn't this thought experiment clearly show that if we maintain that FTL communication is ruled out, we must also rule out "universal collapse" in the Copenhagen interpretation? EDIT: Here is an example of an explicit experiment (though I think experts could come up with something better): You can entangle a photon with an electron such that the angle of the photon is correlated with the electron's position at each slit of a double slit experiment. If the photon is detected (it's outgoing angle measured), then which-path information is known, and there is no interference. If the photon is not detected, the interference remains. The experiment is designed such that the photon and electron go in roughly opposite directions, apart from the tiny deflection which gives which-path information. You set up a series of photon detectors 100 ly away on one side, and your double slit experiment 100 ly away in the opposite direction. Now you produce the entangled pairs in bunches, say of 100 entangled pairs, each coming every millisecond, with a muon coming between each bunch to serve as a separator. Then the idea is that someone at the photon detector side can send information to someone watching the double-slit experiment, by selectively detecting all of the photons in some bunches, but not in others. If all of the photons are detected for one bunch, then the corresponding electron bunch 200 ly away should show no interference effects. If all of the photons are not detected for one bunch, then the corresponding electron bunch 200 ly away would show the usual double-slit interference effects (say on a phosphorus screen). (Note that this does not require combining information from the photon-detector-side with the electron-double-slit side in order to get the interference effects. The interference effects would visibly show up as the electron blips populate the phosphorus screen, as is usual in a double-slit experiment when which-path information is not measured.) In such a way the person at the photon detectors can send '1's and '0's depending on whether they measure the photons in a given bunch. Suppose they send 'SOS' in Morse code. This requires 9 bunches, and so this will take 900 milliseconds, which is less than 200 years. The point is that such an experiment would only work if you assume that the measurement of the photon really does collapse the wave function nonlocally. | Take a sponge ball and compress it. The net force acting on the body is zero and the body isn't displaced. So can we conclude that there is no work done on the ball? | eng_Latn | 4,046 |
I read in a book that () 160 qubits (quantum bits) could hold $2^{160} \approx1.46\times 10^{48}$ bits while the qubits were involved in computation." How does this calculation come about? The context of the statement is that a caffine molecule would require $10^{48}$ bits to be represented by a classical computer. However a quantum computer would require 160 qubits and is thus well suited for such representation. If I look at this question on Quora, a 512 bit computer (which I suppose are real) would give a largest 155 digit number (). Isn't that big enough to represent atoms, molecules etc.? | I recently read this , which stated: For scientists trying to design a compound that will attach itself to, and modify, a target disease pathway, the critical first step is to determine the electronic structure of the molecule. But modeling the structure of a molecule of an everyday drug such as penicillin, which has 41 atoms at ground state, requires a classical computer with some $10^{86}$ bits—more transistors than there are atoms in the observable universe. Such a machine is a physical impossibility. But for quantum computers, this type of simulation is well within the realm of possibility, requiring a processor with 286 quantum bits, or qubits. Along with this resource estimate for penicillin, I've also seen of the number of qubits required to model the ground state of caffeine (160 qubits). Given that the above report offers no reference(s) (probably in the name of business intelligence) and much Internet searching and looking into the quantum chemistry literature has come up short, my question is: Where are these resource estimates coming from – is there a journal article that published these numbers? I would really like to identify the methodology and assumptions used in making these estimates. | I recently read this , which stated: For scientists trying to design a compound that will attach itself to, and modify, a target disease pathway, the critical first step is to determine the electronic structure of the molecule. But modeling the structure of a molecule of an everyday drug such as penicillin, which has 41 atoms at ground state, requires a classical computer with some $10^{86}$ bits—more transistors than there are atoms in the observable universe. Such a machine is a physical impossibility. But for quantum computers, this type of simulation is well within the realm of possibility, requiring a processor with 286 quantum bits, or qubits. Along with this resource estimate for penicillin, I've also seen of the number of qubits required to model the ground state of caffeine (160 qubits). Given that the above report offers no reference(s) (probably in the name of business intelligence) and much Internet searching and looking into the quantum chemistry literature has come up short, my question is: Where are these resource estimates coming from – is there a journal article that published these numbers? I would really like to identify the methodology and assumptions used in making these estimates. | eng_Latn | 4,047 |
After reading an article on Schrodinger's Cat, it seems that if we take the environment as an observer, that superposition cannot occur because all atomic and subatomic entities would be observed all the time. Thus, something like quantum entanglement cannot occur. So if superposition cannot occur, why is superposition (and by extension quantum entanglement) still part of quantum mechanics? Updated: In the question , the notion of observer is replaced by measurement. In this context, my question would be: if the system (cat) is constantly being measured by the environment (the observer is watching the cat), how can superposition (the cat is in multiple states; i.e., alive and dead) exist in quantum mechanics? For example, if a photon passes by a heavy particle and splits into an electron and positron, the splitting process is a measurement of the electron and positron to make sure the total spin is 0. I understand the argument that we might not know which has +1/2 and which has -1/2, but the observation/measurement had to be done to make sure we didn't have 3/4 total spin. | I don't understand how quantum mechanics (and therefore also quantum computers) can work given that while we work with quantum states, particles that this quantum state consist of cannot be observed, which is the most fundamental requirement. If I am not mistaken, by "observed" we mean interaction with any other particle (photon, gluon, electron or whatever else). So my very important questions: Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse? Aren't all particles in the universe interacting with Higgs field and gravitons etc? Why doesn't that cause every quantum state to collapse? I feel there is something very fundamental in quantum mechanics that I am not aware of, hence I would be very pleased to have these questions answered. | I think that is pretty good prima-facia evidence that is just facilitating the deposition of crap. | eng_Latn | 4,048 |
The trick of quantum computing is to take the advantage of wave mechanics (superposition) and entanglement. This allows to perform parallel computations/manipulations with $2^n$ superposed waves for $n$ bits. This principle does not rely on quantum mechanics. Superposed waves do also exist in classical mechanics (although I am not sure we can make the number of tones also scale exponentially with the size, but there could be some profit). Are there examples of efforts to create classic analogues of quantum computers that use superposed waves and manipulate those, instead of using bits in silicon chips? (I do not mean efforts to create a virtual quantum computer) This question might be generalized. Are/were there any efforts to try to move away from binary computers? | The intuition I have for why quantum computing can perform better than classical computing is that the wavelike nature of wavefunctions allow you to interfere multiple states of information with a single operation, which theoretically could allow for exponential speedup. But if it really is just constructive interference of complicated states, why not just perform this interference with classical waves? And on that matter, if the figure-of-merit is simply how few steps something can be calculated in, why not start with a complicated dynamical system that has the desired computation embedded in it. (ie, why not just create "analog simulators" for specific problems?) | I was wondering if quantum particles do actually exists in two different states simultaneously and if it has been proven they do indeed exists in a superposition of states. How has it been figured out since observing it would collapse the wave-function into one single state (two superposition of states into one ) as it has been mentioned in the Schrodinger's cat experiment? | eng_Latn | 4,049 |
I am starting to step into the field of Topological Quantum Information and Computation and am in search of tools which I can use to directly simulate or realize these transformations in a textual or graphical manner. | Does something like exist for topological (eg. braided) circuits? Alternatively, any ideas on how @ is getting (or something similar)? | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 4,050 |
In chapter 1 of Quantum Computation and Quantum Information by Michael A. Nielsen & Isaac L. Chuang, I came across this paragraph on quantum teleportation, Intuitively, things look pretty bad for Alice. She doesn’t know the state $\lvert\psi\rangle$ of the qubit she has to send to Bob, and the laws of quantum mechanics prevent her from determining the state when she only has a single copy of $\lvert\psi\rangle$ in her possession. What’s worse, even if she did know the state $\lvert\psi\rangle$, describing it precisely takes an infinite amount of classical information since $\lvert\psi\rangle$ takes values in a continuous space. So even if she did know $\lvert\psi\rangle$, it would take forever for Alice to describe the state to Bob. So Alice and Bob share a qubit each from an EPR pair created long ago and now Alice wishes to teleport the state $\lvert\psi\rangle$ to Bob by only sending classical information. I do not understand why describing $\lvert\psi\rangle$ takes an infinite amount of classical information, since to my knowledge, only the amplitudes of the basis vectors need to be known($\lvert\psi\rangle=\alpha \lvert 0\rangle+\beta \lvert 1\rangle$). Maybe I did not understand properly what it means for Alice to know a state $\lvert\psi\rangle$. Any guidance would be helpful. Thank you. PS: I'm not from a Quantum mechanics background. | I have two question concerning information content of qubit. Question 1: How many classical bits are needed to represent a qubit: A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\beta \end{pmatrix}, ~~ \alpha, \beta \in \mathbb{C}$. So, we need four real numbers to represent it. But when facts that (i) $|\alpha|^2+|\beta|^2 = 1$ and (ii) two qubits which differ in global phase only are indistinguishable, are taken into account, only two real numbers are necessary (angles on Bloch sphere). Moreover, we can choose a precission of the qubit representation (i.e. number of decimal places in $\alpha$ and $\beta$ or Bloch sphere angles) which influence number of classical bits needed to described the qubit. So, it seems to me that the qubit representation cannot be used for measuring qubit information content but only memory consumption in simulation. Am I right? Question 2: What is an (effective) information content of qubit: A superdense coding enable us to send two classical bits via one qubit. But on the other hand you need two entangled qubits prepared in advance. Given these facts, what is an information content of qubit? One or two classical bits? Or do I need to use another angle of view given the fact that qubits are "continuous" (i.e. described by complex numbers $\alpha$ and $\beta$)? | Take a sponge ball and compress it. The net force acting on the body is zero and the body isn't displaced. So can we conclude that there is no work done on the ball? | eng_Latn | 4,051 |
How can quantum disjuction be illustrated? | The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g., x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which , while . | Compass-M1 transmits in 3 bands: E2, E5B, and E6. In each frequency band two coherent sub-signals have been detected with a phase shift of 90 degrees (in quadrature). These signal components are further referred to as "I" and "Q". The "I" components have shorter codes and are likely to be intended for the open service. The "Q" components have much longer codes, are more interference resistive, and are probably intended for the restricted service. IQ modulation has been the method in both wired and wireless digital modulation since morsetting carrier signal 100 years ago. | eng_Latn | 4,052 |
Mathematically what is the difference between pure separable state and entangled state ? Can anyone explain with equations? | I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far: superposed: A superposition of two states which a system $A$ can occupy, so $\frac{1}{\sqrt{2}}(|0\rangle_A+|1\rangle_A)$ seperable: $|1\rangle_A|0\rangle_B$ A state is called separable, if its an element of the (tensor)product basis of system $A$ and $B$ (for all possible choices of bases) entangled: $\frac{1}{\sqrt{2}}(|0\rangle_A|1\rangle_B+|1\rangle_A|0\rangle_B)$ is not a state within the product basis (again for all possible bases). mixed state: Is a statistical mixture, so for instance $|1\rangle$ with probability $1/2$ and $|0\rangle$ with probability $1/2$ pure state: Not a mixed state, no statistical mixture I hope that the above examples and classifications are correct. If not it would be great if you could correct me. Or add further cases, if this list is incomplete. On wikipedia I read about Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero. which is perfectly fine. However I also read on wikipedia a criterion for : Another, equivalent, criterion is that the von Neumann entropy is 0 for a pure state, and strictly positive for a mixed state. So does this imply that if I look at the subsystems of an entangled state, that they are in a mixed state? Sounds strange... What would be the statistical mixture in that case? Moreover I also wanted to ask, whether you had further illustrative examples for the different states I tried to describe above. Or any dangerous cases, where one might think a state of one kind to be the other? | I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far: superposed: A superposition of two states which a system $A$ can occupy, so $\frac{1}{\sqrt{2}}(|0\rangle_A+|1\rangle_A)$ seperable: $|1\rangle_A|0\rangle_B$ A state is called separable, if its an element of the (tensor)product basis of system $A$ and $B$ (for all possible choices of bases) entangled: $\frac{1}{\sqrt{2}}(|0\rangle_A|1\rangle_B+|1\rangle_A|0\rangle_B)$ is not a state within the product basis (again for all possible bases). mixed state: Is a statistical mixture, so for instance $|1\rangle$ with probability $1/2$ and $|0\rangle$ with probability $1/2$ pure state: Not a mixed state, no statistical mixture I hope that the above examples and classifications are correct. If not it would be great if you could correct me. Or add further cases, if this list is incomplete. On wikipedia I read about Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero. which is perfectly fine. However I also read on wikipedia a criterion for : Another, equivalent, criterion is that the von Neumann entropy is 0 for a pure state, and strictly positive for a mixed state. So does this imply that if I look at the subsystems of an entangled state, that they are in a mixed state? Sounds strange... What would be the statistical mixture in that case? Moreover I also wanted to ask, whether you had further illustrative examples for the different states I tried to describe above. Or any dangerous cases, where one might think a state of one kind to be the other? | eng_Latn | 4,053 |
I'm not an expert and I don't know if already exists something like the following model, but I wrote a simple (mental) model to understand the basic concepts of quantum mechanics. I want to know if this model is valid or not. Red-or-Black (RoB) Card Model Suppose to have two cards, one is red and the other is black. Both the cards have the other side with the same color (e.g. white). A special machine can shuffle the cards truly random and then puts the cards turned down on the table with only the backs visible (i.e. the white side). Nobody knows where is the red and the black card, so each card is red or black with the 50% of probability. In other words each card is red and black at the same time (superposition). This model seems work because when you turn up one of the two cards (measurement), you're fixing its state to a single state (or red or black). At the same time you're fixing also the state of the other card (entanglement). If you repeat the measure turning down and then turning up one of the two cards the result is always the same (the state is fixed). Also the no-cloning theorem works because you can't copy the color of a card until you turn up the card. Is this correct? Another strange thing is the observer definition. If I view the color of a card I'll fix its state, but this is valid also if my cat views the color of that card. So, who/what is the observer? Can be the card itself? The card have the color printed over its surface, so the card knows its state, then I can't understand if it's right to say that the card is in a superposition because the state should be already fixed by itself (i.e. there is only a single state). | Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, until they look at them (measure). If the observer A looks at his ball he will see its color, which is white, so he immediately knows the color of the second ball. Lets call this “classical entanglement”. My question is: What is the difference between this “classical entanglement” and the quantum entanglement, for example, of two entangled electrons with opposite spins states? Can this analogy be used to explain the quantum entanglement? | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 4,054 |
Please post further comments or answers to The probability that an initial quantum state $|\psi_i\rangle$ evolves to become the final quantum state $|\psi_f\rangle$ is given by \begin{eqnarray} P_{i \rightarrow f} &=& |\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle|^2 \tag{1}\\ &=& \langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle^*\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \\ &=& \langle\psi_i|U^\dagger_{i \rightarrow f}|\psi_f\rangle\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \\ &=& \langle\psi_i|U_{f \rightarrow i}|\psi_f\rangle\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \end{eqnarray} where $U_{i \rightarrow f}$ is the forward-time evolution operator and $U_{f \rightarrow i}=U^\dagger_{i \rightarrow f}$ is the corresponding backward-time evolution operator. Equation (1) seems to show that the probability $P_{i\rightarrow j}$ can be interpreted as the system first evolving forwards in time and then evolving backwards in time. Perhaps this is an example of Murray Gell-Mann's that "Everything not forbidden is compulsory"? At the quantum level, below observable probabilities, there is nothing to stop time flowing both forwards and backwards. Does this reasoning help to explain the Born rule? | The probability that an initial quantum state $|\psi_i\rangle$ becomes the final quantum state $|\psi_f\rangle$ is given by \begin{eqnarray} P(i \rightarrow f) &=& |\langle\psi_f|\psi_i\rangle|^2 \tag{1}\\ &=& \langle\psi_f|\psi_i\rangle^*\langle\psi_f|\psi_i\rangle \\ &=& \langle\psi_i|\psi_f\rangle\langle\psi_f|\psi_i\rangle. \end{eqnarray} Equation (1) seems to show that the probability for the transition ($i\rightarrow f$) can be interpreted as the system both moving forward in time ($i\rightarrow f$) with amplitude $\langle\psi_f|\psi_i\rangle$ and backward in time ($f\rightarrow i$) with amplitude $\langle\psi_i|\psi_f\rangle$ simultaneously. Does this reasoning help to explain the Born rule? (Is it like the Transactional Interpretation of QM?) I guess we must experience the macroscopic direction of time ($i\rightarrow f$) in accord with increasing entropy in an expanding universe whereas microscopically QM works both forwards and backwards in time. Addition This is an improved version of the argument including time-evolution operators. The probability that an initial quantum state $|\psi_i\rangle$ evolves to become the final quantum state $|\psi_f\rangle$ is given by \begin{eqnarray} P_{i \rightarrow f} &=& |\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle|^2 \tag{2}\\ &=& \langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle^*\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \\ &=& \langle\psi_i|U^\dagger_{i \rightarrow f}|\psi_f\rangle\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \\ &=& \langle\psi_i|U_{f \rightarrow i}|\psi_f\rangle\langle\psi_f|U_{i \rightarrow f}|\psi_i\rangle \end{eqnarray} where $U_{i \rightarrow f}$ is the forward-time evolution operator and $U_{f \rightarrow i}=U^\dagger_{i \rightarrow f}$ is the corresponding backward-time evolution operator. Equation (2) seems to show that the probability $P_{i\rightarrow j}$ can be interpreted as the system first evolving forwards in time and then evolving backwards in time. Perhaps this is an example of Murray Gell-Mann's that "Everything not forbidden is compulsory"? At the quantum level, below observable probabilities, there is nothing to stop time flowing both forwards and backwards. | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 4,055 |
When was Leibniz an active philosopher? | German philosophers have helped shape western philosophy from as early as the Middle Ages (Albertus Magnus). Later, Leibniz (17th century) and most importantly Kant played central roles in the history of philosophy. Kantianism inspired the work of Schopenhauer and Nietzsche as well as German idealism defended by Fichte and Hegel. Engels helped develop communist theory in the second half of the 19th century while Heidegger and Gadamer pursued the tradition of German philosophy in the 20th century. A number of German intellectuals were also influential in sociology, most notably Adorno, Habermas, Horkheimer, Luhmann, Simmel, Tönnies, and Weber. The University of Berlin founded in 1810 by linguist and philosopher Wilhelm von Humboldt served as an influential model for a number of modern western universities. | In a famous paper of 1936 with Garrett Birkhoff, the first work ever to introduce quantum logics, von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic structure for quantum logics. The concept of creating a propositional calculus for quantum logic was first outlined in a short section in von Neumann's 1932 work, but in 1936, the need for the new propositional calculus was demonstrated through several proofs. For example, photons cannot pass through two successive filters that are polarized perpendicularly (e.g., one horizontally and the other vertically), and therefore, a fortiori, it cannot pass if a third filter polarized diagonally is added to the other two, either before or after them in the succession, but if the third filter is added in between the other two, the photons will, indeed, pass through. This experimental fact is translatable into logic as the non-commutativity of conjunction . It was also demonstrated that the laws of distribution of classical logic, and , are not valid for quantum theory. | eng_Latn | 4,056 |
Identifying a story about a boy who travels to a mirrored universe with ketchup that makes you intoxicated There was a novel I read back in the day about a boy who travels back and forth between a mirror-image of our universe. I am afraid I cannot recall much about the plot, except that mirrored food is inedible and when mirrored ketchup packets were brought back from the other universe they taste like chocolate and mess you up. Could someone help me identify this book? After going through organic chemistry back in college, I think it should be required reading for any writer who has a story where the characters land on alien planets and find everything to be edible. | ID a book about a mirror world and 4th dimension I read a book about 10-15 years ago about a boy and a girl who find a mirror. What made the mirror special was, they were able to enter the reflection and be a part of the reverse image world. They end up going to school and when asked to write something on the board, it ends up being backwards, but to them looks normal. Later, the two end up in a world with 4 dimensions. With the added dimension they can't see as they normally could. If one moved a certain way the other would see their insides. Eventually a native of that dimension made some type of device that lets them see regularly. Other than that my memory is blank. If I remember anything else I will be sure to edit it in. | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,057 |
How does cold fusion work? I understand that in regular fusion, you use high levels of heat to accelerate atoms to speeds high enough to overcome nuclear force. What method would be used to achieve ? | Why is cold fusion considered bogus? Cold fusion is being mentioned a lot lately because of some new setup that apparently works. This is an unverified claim. See for example: ( of that last link in the Wayback Machine, given frequent from that page.) While we should give the scientific community time to evaluate the set up and eventually replicate the results, there is undoubtedly some skepticism that cold fusion would work at all, because the claim is quite extraordinary. In the past, after Fleischmann and Pons announced their cold fusion results, in perfectly good faith, they were proven wrong by subsequent experiments. What are the experimental realities that make Fleischmann and Pons style cold fusions experiments easy to get wrong? Would the same risks apply to this new set up? | What does a "real" quantum computer need for cryptanalysis and/or cryptographic attack purposes? The cryptographic world has been buzzing the word "quantum" for a while now (even the NSA is currently preparing itself for a post-quantum crypto world) and quantum-related hardware engineering is evolving constantly. For example: the 5-qubit quantum computer created at MIT by using the technique of ion traps succeeded in prime-factorizing 15. Does that mean that since it succesfully managed that, that it is a all-purpose quantum computer which could be used for cryptanalysis and/or cryptographic attacks? If that's not the case, what exactly would a "real" quantum computer need (think: rough description of expected technical abilities, aka specs) to enable its users to use it for cryptanalysis and/or cryptographic attack purposes? And - ignoring rumours about potentially existing but confidential governmental projects - does any such system already exist today? | eng_Latn | 4,058 |
Meaning of principal components I have difficulty understanding the meaning of the Principal Components (PC) - On one hand, PC are computed by finding loading vectors that maximize the variance, but on the other hand I read another interpretation that says PC are the closes to the n-observations. It seems to me like there is a contradiction, how are they closest if they have the highest variance?.. In general, when do we know to stop at the first PC and not go for the second one? Thanks | Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? I have carried out a principal components analysis of six variables $A$, $B$, $C$, $D$, $E$ and $F$. If I understand correctly, unrotated PC1 tells me what linear combination of these variables describes/explains the most variance in the data and PC2 tells me what linear combination of these variables describes the next most variance in the data and so on. I'm just curious -- is there any way of doing this "backwards"? Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | eng_Latn | 4,059 |
If we can predict the quantum leap, won't that render quantum computers useless? Recent news from Yale... We can predict the quantum leap before the particle collapses its superposition. We can even change it to whichever position we like in real time. In layman terms, as I understand with my limited knowledge, Schrodinger's cat can be SAVED. But... Also to my limited knowledge, the core of how a quantum computer works is because of its superposition feature and its uncertainty. Then put these two paragraphs together... If the superposition is now old news, so would quantum computers. Right? What am I missing here? | Does the new finding on "reversing a quantum jump mid-flight" rule out any interpretations of QM? new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are and . I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding. The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work? | Tsunami dampening mechanisms Encouraged by the zeitgeist let me ask the following: Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it reaches the coast itself? The following picture comes to mind. We have some device which is small enough to be mounted on a buoy. An array of such buoys can be anchored some distance off the coastline, controlled by computers which are linked into the global tsunami warning network. This setup is quite feasible given what a cell phone can do today. On the detection of an oceanic earthquake or other tsunami generating event (such as a piece of the Rock of Gibraltar falling into the sea) and given present environmental conditions one can calculate the expected path of the tsunami and its intensity. If a TDS (Tsunami Dampening System) of the type I describe above happens to be deployed in range of the tsunami, all relevant information is conveyed to the TDS controllers by the global tsunami warning system. All this happen in a matter of moments. This leaves plenty of time (25min - 2hr) for the devices in the TDS array to be activated and to do their job. The question in this case would be - what form could such devices take? Perhaps mini-turbines which could dissipate the incoming energy into the ocean by first converting it to electrical energy. Any such undertaking involves physical estimates for the size and shape of such an array, the precise capabilities of each device, etc. Many of these concerns involve simple physical questions. Can you come up with the details of such a system or alternatively outline your own design? If you think that this idea would never work in the first place - for technological, physical or some other reasons - please explain what you think would be the prime obstacle and why? | eng_Latn | 4,060 |
What's stopping two independent observers from measuring the speed and position at the same time, separately? From This means, it doesn't take into account, the Uncertainty Principle of Quantum Mechanics, which says that an object can not have both a well defined position, and a well defined speed: the more accurately one measures the position, the less accurately one can measure the speed, and vice versa. Why can't two people agree to measure the same particle? One measures the speed and the other the position. I suppose it raises the question - how do you "agree" on which particle to measure. But that may be part of the answer to this question. | Uncertainty principle and multiple observers My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa. Say there is such an observer, interested in the precise position of a particular particle. Now, consider a second, independent observer, unbeknownst to the first, who is trying to measure the exact momentum of the same particle without caring about the position. As a thought experiment, we assume that the two observers are somehow able to access the same particle at the same time in some way without being aware of each other. Can both observers get their desired results? | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | eng_Latn | 4,061 |
Atoms: boson or fermion? The spin of fundamental particles determines if they are bosons or fermions. The atoms also have bosonic or fermionic behavior, for example $\require{mhchem}\ce{^4He}$ has bosonic and $\ce{^3He}$ has fermionic statistics. Which quantity of atom determines its statistics? | Huge confusion with Fermions and Bosons and how they relate to total spin of atom I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, and each fermion has a 1/2 spin. Since there are an even number of fermions, the total spin value is an integer. This spin number is the "intrinsic" spin number that cannot be changed, but its orientation "up" or "down" can be changed. For atomic Hydrogen, it is a Boson because it has integer spin, however it also has a single electron. I read on physics forums, , that the spin of atom comes from the electrons and not its nucleus. I also read on here, , that the spin of atomic Hydrogen is 1/2! The answer says atomic Hydrogen has spin 1/2 because it ignores the nuclear spin. This is one thing that is confusing me. Shouldn't atomic Hydrogen have an integer spin because of the nuclear component? So does atomic Hydrogen have spin and is affected by a magnetic field? Nuclear spins are affected by magnetic fields, but they aren't as affected as electrons according to the discussion on physics forums. Why do we ignore nuclear spin sometimes? Also, can someone help me out here with all the possibilities? Is there a Boson with an half integer spin value? (Surely, there must not be) However atomic Hydrogen is one of those cases! (It seems...) (Why don't we cancel out the nuclear spin with the electron spin?) Say we have another atom that is a Boson, It has unpaired electrons in different orbitals, so what determines whether or not electrons fill in orbitals as spin up or down? Does spin down nuclear spin cancel out a electron up spin? | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | eng_Latn | 4,062 |
How does an outcome of photon measurement 1 affect Photon 2 in quantum entanglement? I know I am missing something and this question is probably very silly, but I would like to understand. Quoting an article: If one photon is measured to be in a +1 state, the other must be in a -1 state. Since the outcome of one photon affects the outcome of the other, the two are said to be entangled.......when you measure the state of one photon you immediately know the state of the other....If we’re light years apart, we each know the other’s outcome for entangled pairs of photons, but the outcome of each entangled pair is random (what with quantum uncertainty and all), and we can’t force our photon to have a particular outcome. I just cannot see the "magic" here. Using a stupid analogy: There are two balls, black and white, wrapped in a piece of cloth. You take one and I take the other. Whenever and wherever I unwrap the one I took, I will immediately know which one you have. What is so special about that in the world of particles, how does the outcome of the first affect the other? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | Why can we apply the $E=hf$ equation for electrons? So in my textbook, it states that the $E=hf$ equation applies to electrons, and all particles, not just photons. But in order to prove this, wouldn't these particles need to have zero mass, to satisfy $E=pc$ from Einstein's equation? In Einstein's theory of relativity $E^2= p^2c^2 + m^2c^4$, we get $E=pc$ because we consider the mass to be zero. For $E=hf$ to work for other particles, don't we need to assume electrons have zero rest mass? | eng_Latn | 4,063 |
Choosing a book to gain general knowledge about biology I will be first year undergraduate at Physics department next year and last year I was at the Medicine faculty. I want do double major in the second year of faculty with Molecular Biology and Genetics. The intersection of biology and physics is my interest. I have two books about biology, first one is What is Life?-Mind and Matter by Erwin Schrödinger and the second one is This is Biology by Ernst Mayr. Which one should I read to acquire general knowledge about Biology? | Introductory biology text for an outsider I'm a maths major and I have an interest in learning biology. I know very, very little; I know how babies are made and that's about it. Could anyone recommend a stimulating text to read for its own sake and also to use to learn biology? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,064 |
I got "BEGIN PGP PUBLIC KEY BLOCK" attached to an email and I don't know what it is Okay, I have no clue what this is, but I just received an email that has this in it. -----BEGIN PGP PUBLIC KEY BLOCK----- [redacted] -----END PGP PUBLIC KEY BLOCK----- If this means something, could someone decode it for me? If not, then could someone just tell me what it is? | what is PGP public key block? There's PGP public key block posted on some websites (eg. ). It's not hex code. it uses much more alphabet characters. What is it? Why is this information posted? how can i use it? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,065 |
Band gap in semiconductors If one semiconductor is transparent and another is not (in the visible spectrum), what causes that difference? Is it related to their band gap, because that influences which wavelengths they can emit? As an example gallium arsenide is opaque, zinc sulphide isn't. | Why is diamond transparent while graphite is not? Diamond and graphite are both made of the same atom, carbon. Diamond has a tetrahedron structure while graphite has a flat hexagonal structure. Why is diamond transparent while graphite is not (at least not with more than a couple of layers)? | What counts as "observation" in Schrödinger's Cat, and why are superpositions possible? So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must be in a superposition of dead and alive. This makes sense at first, but the state of the cat inside the box will affect the outside world in an observable way, right? For example if the cat dies, it might meow loudly which would be audible. If it didn't meow, it would produce a thud on the ground when it dies. And even if the ground was very solid, the redistribution of mass inside the box will affects its gravity field which means the whole universe theoretically immediately observe's the cat's death. So extending this argument to all superpositions, the different states would cause different effects on the rest of the universe, usually a slight change in the gravity field is the minimum. This gravity perturbation would propagate throughout the universe, and even all the experimenters go to sleep with thick, thick earplugs, somebody or something in the universe is going to inadvertently observe the event and the superposition immediately collapses. Thus superpositions cannot exist beyond an extremely short amount of time. What's wrong with my reasoning? | eng_Latn | 4,066 |
How does the red pill work? When Neo takes the red pill all kinds of things start to happen. In the matrix the mirror turns into 'The Blob' and smothers his body, in the real world he claws his way through his pod membrane, a machine suddenly appears and grabs him and looks him over then the control cables are detach from his spine and he's flushed to the sewer. How does that work? For clarification; The two other related questions' answers talk about placebos, metaphors, sleeping pills and finally "a program to wake Neo up". Good answers for the context of those questions but they all focused on 'Neo', no explanation to what physically happens and how it happened. Is it a virus designed to cause the machine nursemaid to 'abort' the infection? | Does either pill actually do anything? When Morpheus offers the pill choice to Neo, they are still in the Matrix. That leads me to belive that none of the pills are real thus having no particular effect in the real world. Was it some sort of placebo effect that freed Neo from the Matrix or do the pills have an actual effect? | What would be an informative introduction to quantum computing software? I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc). In the question below they are looking for courses on the subject, which I am also interested in, and do plan on checking those links out for ideas. What I am looking for are simple videos, articles, or even games, that cover basic quantum theory at an introductory level. There are some games I have looked into and played. Hello Quantum! was fun and informative, though on my end there was still a lack of comprehension on how the quantum computer (or anything else "quantum") would actually function and play out. My focus for the educational platform is more directed towards the software side of quantum computing. Is there anything that gives a good introduction to the functions and uses a quantum computer will have? As well as what language would be best to program one? Also, would there be a way to program a quantum computer through a classical computer? And, is there a simple introduction to any of this already existing? | eng_Latn | 4,067 |
Has anyone tried any quantum computing programming code that shows or demonstrates the advantage of a quantum computer over classical computers? Thanks a lot. | It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks. One of the most commonly cited examples of a problem in which quantum computers would outperform classical devices is $\text{Factoring}$, but then again, it is also not known whether $\text{Factoring}$ is also efficiently solvable with a classical computer (that is, whether $\text{Factoring}\in \text{P}$). For other commonly cited problems in which quantum computers are known to provide an advantage, such as database search, the speedup is only polynomial. Are there known instances of problems in which it can be shown (either proved or proved under strong computational complexity assumptions) that quantum computers would provide an exponential advantage? | I have been trying to show these two inequalities hold for all positive integers n, but I don't know how to proceed at all... I have tried playing around with them but I didn't find anything helpful. I have also tried induction but I couldn't make it work. | eng_Latn | 4,068 |
Let's say I have a time independent Hamiltonian so my system conserves energy. It's initially in an energy eigenstate with $E=1$ in whatever energy units you like. I measure a different observable that doesn't commute with $H$, then I measure $H$ again. I have some probability now of finding my system in an energy eigenstate with $E\neq1$. What gives? If this was a harmonic oscillator for example, it could be the case that I end up in a state with hugely more energy. Where does this extra energy come from? In this question, the accepted answer says that the probe particle imparts the energy: I get that idea, but after the probe interacts with the system and I measure the energy again, then my energy may go down, stay the same or go up. How does this relate to the energy of the probe particle? I feel I'm missing something fundamental here. | Consider a particle in a potential well. Let’s assume it’s a simple harmonic oscillator potential and the particle is in its ground state with energy E0 = (1/2) ℏω0. We measure its position (measurement-1) with a high degree of accuracy which localises the particle, corresponding to a superposition of momentum (and therefore energy) states. Now we measure the particle’s energy (measurement-2) and happen to find that it’s E10 = (21/2) ℏω0. Where did the extra energy come from? In the textbooks it’s claimed that the extra energy comes from the act of observation but I wonder how that could work. Measurement-1 which probed the position of the particle can’t have delivered to it a precise amount of energy, while measurement-2 might just have been passive. No doubt there is entanglement here between the particle state and the measuring device but where, and which measurement? | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 4,069 |
It seems that a hidden variables theory could reproduce Bell's experiments results, preserving locality, as long as it accepts that the superposition state(or at least a faux superposition) existed at $t=0$ of the creation of entangled pair. In this case, the question "where and how were the particles previous to the measurement?" makes sense, but only up to the moment they were defined to be opposites. It could be that, while movement over time for a entangled particle is also described by a wave function, its spin for each vector remains constant over time (when considering the same direction measured), only being uncertain at t=0. There's even a global vertical direction that could be responsible for this: gravity. Bell, in fact, accepts that $\vec\lambda\cdot\vec p >0$ could properly describe the possibly states for a single particle in a local hidden variable theory. Why can't it be that when the entangled pair is created, this measurement is ran over in a particle, which defines every possible vector for this particle (respecting the probability), then the result is transferred and reversed in the other particle? That's all this local hidden theory would need to accept. In this case, the particles only communicate at $t=0$, and never again. | Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality. While I don't fully understand it, Leggett's inequality takes this a step further and shows that we can't even have non-local realism theories. Apparently there are some hidden variable theories that get around this by having measurements be contextual. I've heard there are even inequalities telling us how much quantum mechanics does or doesn't require contextuality, but I had trouble finding information on this. This is all confusing to me, and it would be helpful if someone could explain precisely (mathematically?) what is meant by: realism, locality (I assume I understand this one), and contextuality. What combinations of realism, locality, and contextuality can we rule out using inequality theorems (assuming we have experimental data)? | It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect the state of the entangled partner. For example, if Alice and Bob share an entangled pair of electrons and Alice measures her spin in the $x$ direction, then Bob's spin will also end up spinning in that direction, and similarly if she measures in the $z$ direction. Moreover, the effect will be instantaneous, regardless of the spatial distance between the two particles, which seems at odds with special relativity. Can I use a scheme like this to communicate faster than light? | eng_Latn | 4,070 |
why are qubits such a game changer in quantum computing? Qubits are in a superposition which means that they can currently be both digits of 1 and 0 at the same time BUT this is my question: If Qubits have to be filtered to be used then what makes them better than normal bits after they are filtered? they are going to become 1 OR 0 because they can't be used in their superposition (If I'm correct), so the way I see it they are just normal bits we just have to take the extra time to filter first. It would be much more efficient (the way I see it) to simply re-arrange bits (like 1001 to 1100 or 1010 they use the same bits but get multiple results) to get faster results ya-know? So if someone could tell me why quantum computing is so much better I would appreciate it a lot! If I said anything wrong than please correct me! | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | What are the advantages of 10-bit monitors? To support 10-bit color the following are needed: A monitor supporting it. A GPU supporting it (only AMD FirePro and NVIDIA Quadro support this?). Compatible software. Unless I am mistaken there are very few programs out there supporting 10-bit color. Photoshop is a notable example. The questions are about how 10-bit monitors perform in comparison with 8-bit monitors: In which situations would a 10-bit monitor give a noticeable advantage over an 8-bit monitor (say, for professional photography)? Have 10-bit monitors been compared against 8-bit monitors based on subjective or objective tests? What were the results? Human eyes can see only 10m colors, so would using a monitor with 1b colors make a difference? | eng_Latn | 4,071 |
Logical table of P->Q math statements In a course I had, we have been given two statements P and Q and their "boolean table" : While I completely understand P and Q and P or Q values, I can't understand the first two lines for P->Q, why is the result true even when P is false ? Thank you. | In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False? I am studying entailment in classical first-order logic. The Truth Table we have been presented with for the statement $(p \Rightarrow q)\;$ (a.k.a. '$p$ implies $q$') is: $$\begin{array}{|c|c|c|} \hline p&q&p\Rightarrow q\\ \hline T&T&T\\ T&F&F\\ F&T&T\\ F&F&T\\\hline \end{array}$$ I 'get' lines 1, 2, and 3, but I do not understand line 4. Why is the statement $(p \Rightarrow q)$ True if both p and q are False? We have also been told that $(p \Rightarrow q)$ is logically equivalent to $(~p || q)$ (that is $\lnot p \lor q$). Stemming from my lack of understanding of line 4 of the Truth Table, I do not understand why this equivalence is accurate. Administrative note. You may experience being directed here even though your question was actually about line 3 of the truth table instead. In that case, see the companion question And even if your original worry was about line 4, it might be useful to skim the other question anyway; many of the answers to either question attempt to explain both lines. | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,072 |
Any alternative to time? Just curious to know. Suppose physicists start from the very beginning, i.e defining the fundamental quantities, figuring out the math etc. So will they see the universe differently than what we have presently, particularly can we obtain any alternative to time? Why is time given such an importance? Why is time defined as : "Time is what the clock reads"? | What is time, does it flow, and if so what defines its direction? This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as: What do physicists mean by time? How does time flow? Why is there an arrow of time? | What would be an informative introduction to quantum computing software? I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc). In the question below they are looking for courses on the subject, which I am also interested in, and do plan on checking those links out for ideas. What I am looking for are simple videos, articles, or even games, that cover basic quantum theory at an introductory level. There are some games I have looked into and played. Hello Quantum! was fun and informative, though on my end there was still a lack of comprehension on how the quantum computer (or anything else "quantum") would actually function and play out. My focus for the educational platform is more directed towards the software side of quantum computing. Is there anything that gives a good introduction to the functions and uses a quantum computer will have? As well as what language would be best to program one? Also, would there be a way to program a quantum computer through a classical computer? And, is there a simple introduction to any of this already existing? | eng_Latn | 4,073 |
Can quantum computers put computer security in jeopardy? There are many articles about quantum computers describing how powerful they are in computing and that they can solve very complicated equations in a short time. One of the biggest security measures that provide safety for computer security is that sometimes it takes years to break a piece of encrypted data. Will this safety remain after a quantum computing revolution? The question is: Can they do such complicated computing? Is it possible quantum computers put computer security in jeopardy? | What does a "real" quantum computer need for cryptanalysis and/or cryptographic attack purposes? The cryptographic world has been buzzing the word "quantum" for a while now (even the NSA is currently preparing itself for a post-quantum crypto world) and quantum-related hardware engineering is evolving constantly. For example: the 5-qubit quantum computer created at MIT by using the technique of ion traps succeeded in prime-factorizing 15. Does that mean that since it succesfully managed that, that it is a all-purpose quantum computer which could be used for cryptanalysis and/or cryptographic attacks? If that's not the case, what exactly would a "real" quantum computer need (think: rough description of expected technical abilities, aka specs) to enable its users to use it for cryptanalysis and/or cryptographic attack purposes? And - ignoring rumours about potentially existing but confidential governmental projects - does any such system already exist today? | What safety precautions should I take when taking photos in the snow? I’m going to Queenstown, NZ in a couple of weeks and want to take my (very new, very precious) Canon 7D with me. I’ve done a little bit of research on how to protect my baby from cold climate (e.g. ) and found that the biggest problem is probably going to be condensation. Some suggestions have been to place the camera in a plastic bag or letting the camera gradually adjust to the new temperature or placing silica gel in the camera bag to absorb moisture. I am leaning toward the latter at the moment because it sounds like it’s the easiest, so I was just wondering if anyone has had any experience in this matter and could share their wisdom. As an alternative I could take my Canon 350D, as I really wouldn’t care if that got damaged in the snow. However I’m a film student and tend to take just as many videos as photos – hence why I really want to take the 7D. But I would seriously regret it if it got damaged… dilemma! So as I actually haven’t used a question mark in the body of text, I will specify that the question is: What safety precautions should I take when taking photos in the snow? Cheers. | eng_Latn | 4,074 |
Proving which Quantum Mechanics interpretation is correct Let's assume that the existence of gravitons is theoretically proven or they are detected by LHC could one interpretaion be proven correct? | Proving which QM interpretation is correct Let's assume that the existence of gravitons is theoretically proven or they are detected by LHC could one interpretaion be proven correct? | Inexact measurement and wavefunction collapse As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is $\psi(q)=\delta(q-q_0)$ where $q_0$ is result of measurement. Now, in reality measurements are never exact, so the wavefunction should not have that sharp peak. Instead it should be broadened depending on precision of measurement. In this case, can we still introduce an operator, an eigenstate of which would the new wavefunction appear? Is it useful in any way? Or does the new wavefunction depend too much on the way it was measured so that each instrument would have its own operator? How would such opeartor look e.g. for a single-slit experiment? | eng_Latn | 4,075 |
Derive the Arbitrary Projection Operator | Projection operators are defined below, given an arbitrary state | ψ ⟩ . {\displaystyle |\psi \rangle .}
| Use this magic prop to make objects appear, disappear or transform. | eng_Latn | 4,076 |
Light pulses and energy-time uncertainty principle Suppose we have a monochromatic light beam. We put an obstacle between source and observer and remove it repeatedly by certain frequency such that observer sees an oscillating intensity of light. Will the observer see different frequencies or only the original frequency? Does the energy-time uncertainty principle apply in this case? | Uncertainty and wave-trains My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an uncertainty in its wavelength or the wave number? Is not a confined wave-train equivalent to a burst of successive pulses which can have a definite wavelength according to their origin or nature of origin. Next, i understand that the De Broglie relation relates the uncertainty in wavelength to the uncertainty in momentum but what links the finiteness of the wave-train to the uncertainty in position? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,077 |
Why we can't conserve light? All I made up in my mind about light beeing a wave traveling at vertain speed, made me thing of it like something we could store in tehory. So I would assume if I had a box where the inside is made up completly with mirrors, when sending light in and closing the box, this light would keep traveling inside the box, beeing reflected by the mirrors untill we release it again. But afaik this isn't the way it is. So how does it come? Why isn't light working this way? | What longest time ever was achieved at holding light in a closed volume? For what longest possible time it was possible to hold light in a closed volume with mirrored walls? I would be most interested for results with empty volume but results with solid-state volume may be also interesting. | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,078 |
Which book in Asimov's Foundation series describes a video communication system just like our "Zoom" Long ago I read all the books in Asimov's Foundation series. In one of them, people are living alone or very few at a time on separate worlds that are far apart. They communicate via a video system that I remember as being very much like today's "Zoom." I can't find which book that is in. Can anyone help? | Short sci-fi story about Earth blockaded by other human colonies Like the subject: short sci-fi story about Earth blockaded by other human colonies. The best humans have colonized some stellar systems. But they begin to treat humans of earth like inferiors. A war began, colonies won the war and blockaded the earth, but despite this the earth won. Who is the author? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,079 |
How are the photon and electron entangled in this situation? | Creation of entangled electrons | A fiber bundle over Euclidean space is trivial. | eng_Latn | 4,080 |
Understanding the basic concepts of quantum mechanics using a model I'm not an expert and I don't know if already exists something like the following model, but I wrote a simple (mental) model to understand the basic concepts of quantum mechanics. I want to know if this model is valid or not. Red-or-Black (RoB) Card Model Suppose to have two cards, one is red and the other is black. Both the cards have the other side with the same color (e.g. white). A special machine can shuffle the cards truly random and then puts the cards turned down on the table with only the backs visible (i.e. the white side). Nobody knows where is the red and the black card, so each card is red or black with the 50% of probability. In other words each card is red and black at the same time (superposition). This model seems work because when you turn up one of the two cards (measurement), you're fixing its state to a single state (or red or black). At the same time you're fixing also the state of the other card (entanglement). If you repeat the measure turning down and then turning up one of the two cards the result is always the same (the state is fixed). Also the no-cloning theorem works because you can't copy the color of a card until you turn up the card. Is this correct? Another strange thing is the observer definition. If I view the color of a card I'll fix its state, but this is valid also if my cat views the color of that card. So, who/what is the observer? Can be the card itself? The card have the color printed over its surface, so the card knows its state, then I can't understand if it's right to say that the card is in a superposition because the state should be already fixed by itself (i.e. there is only a single state). | Quantum entanglement vs classical analogy Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, until they look at them (measure). If the observer A looks at his ball he will see its color, which is white, so he immediately knows the color of the second ball. Lets call this “classical entanglement”. My question is: What is the difference between this “classical entanglement” and the quantum entanglement, for example, of two entangled electrons with opposite spins states? Can this analogy be used to explain the quantum entanglement? | How is the no-cloning theorem compatible with the fact that fan-out gates work? I have some difficulty with understanding no-cloning theorem. Simply speaking, according to the theorem, it is not possible to copy a quantum state. On the other hand, CNOT gate can be used as so-called fan-out gate which purpose is to copy one qubit to another one, previously in state $|0\rangle$. It seems that these two facts negate each other. My question: How is no-cloning theorem compatible with the fact that fan-out gate works? | eng_Latn | 4,081 |
Can Alice encrypt a message to Bob without hiding anything from Eve? I know that if Alice and Bob both have secret-public key pairs, they can use RSA for example. If we remove the possibility that Alice can know anything which Eve doesn't (ie Alice's secret key), is there an algorithm which makes encryption still possible? (I am new in the topic and haven't been able to find an answer.) | How does asymmetric encryption work? I've always been interested in encryption but I have never found a good explanation (beginners explanation) of how encryption with public key and decryption with private key works. How does it encrypt something with one key and decipher it with another key? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,082 |
Is there a word for when you run into someone and both of you try to avoid each other and fail, repeatedly? It has most certainly happened to all of us at least once: Two people walking along the same narrow pathway in opposite directions walk into each other. There is room for both to pass each other, but person A shifts to their left to avoid B, and B shifts to their right (i.e., A's left) in order to do the same thing, so they're still on a collision course. They both realize the mistake and they both try to correct it by moving to the opposite side they did before, so the problem persists. Rinse and repeat 3 or 4 times until one of the parties realizes: "I'll stick to the left (or right) no matter what, and let him pick the other side!", in a sort of perverse human feedback loop. Is there a word or idiom to describe this situation? | Word for the situation of being unable to pass opposing pedestrian, as you both start to step same direction Is there a word or expression in English, which describes the situation, when you can't pass a stranger, who is walking towards you on the street, because you both start to step the same direction? I'm pretty sure I've heard one once. As I remember, it was including "dancing" reference, but in more specific way. | What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold? The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice). Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector. If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't. Alice and Bob can be spatially separated... What am I misunderstanding? The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol... There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: | eng_Latn | 4,083 |
Modern textbooks on quantum mechanics I'm looking for modern textbooks on quantum mechanics that treat topics such as quantum entanglement , bell's theorem , quantum teleportation , quantum information theory , The Many-world interpretation , decoherence etc . All the textbooks that I can find cover the usual topics only (scattering theory , perturbation , the hydrogen atom etc ) But I can't find a book that mainly address these topics . Are there textbooks that specialize in the aforementioned topics ? If not , What are some pedagogical papers that are useful ? I don't care if the resources are mathematically rigorous or not . I would actually prefer books /papers that use more advanced math than usual. | Learn QM algebraic formulations and interpretations I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some reasonable real world assumptions. However I want to avoid the meticulous maths style and rather read something more meant for physicists (where rigorous proofs aren't needed and things are well-behaved ;) ) I.e. I'd prefer more intuitive resources as opposed to the rigorous texts. Can you recommend some reading to get started? | Do electrons really perform instantaneous quantum leaps? This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict. There are so many questions about this and so many answers, but none of them says clearly if the electron's change of orbitals as per QM can be expressed at a time component or is measurable (takes time or not), or is instantaneous, or if it is limited by the speed of light or not, so or even say there is no jump at all. I have read this question: where Kyle Oman says: So the answer to how an electron "jumps" between orbitals is actually the same as how it moves around within a single orbital; it just "does". The difference is that to change orbitals, some property of the electron (one of the ones described by (n,l,m,s)) has to change. This is always accompanied by emission or absorption of a photon (even a spin flip involves a (very low energy) photon). and where DarenW says: A long time before the absorption, which for an atom is a few femtoseconds or so, this mix is 100% of the 2s state, and a few femtoseconds or so after the absorption, it's 100% the 3p state. Between, during the absorption process, it's a mix of many orbitals with wildly changing coefficients. where annav says: A probability density distribution can be a function of time, depending on the boundary conditions of the problem. There is no "instantaneous" physically, as everything is bounded by the velocity of light. It is the specific example that is missing in your question. If there is time involved in the measurement the probability density may have a time dependence. and where akhmeteli says: I would say an electron moves from one state to another over some time period, which is not less than the so called natural line width. where John Forkosh says: Note that the the electron is never measured in some intermediate-energy state. It's always measured either low-energy or high-energy, nothing in-between. But the probability of measuring low-or-high slowly and continuously varies from one to the other. So you can't say there's some particular time at which a "jump" occurs. There is no "jump". where annav says: If you look at the spectral lines emitted by transiting electrons from one energy level to another, you will see that the lines have a width . This width in principle should be intrinsic and calculable if all the possible potentials that would influence it can be included in the solution of the quantum mechanical state. Experimentally the energy width can be transformed to a time interval using the Heisneberg Uncertainty of ΔEΔt>h/2π So an order of magnitude for the time taken for the transition can be estimated. So it is very confusing because some of them are saying it is instantaneous, and there is no jump at all. Some are saying it is calculable. Some say it has to do with probabilities, and the electron is in a mixed state (superposition), but when measured it is in a single stable state. Some say it has to do with the speed of light since no information can travel faster, so electrons cannot change orbitals faster then c. Now I would like to clarify this. Question: Do electrons change orbitals as per QM instantaneously? Is this change limited by the speed of light or not? | eng_Latn | 4,084 |
Canonical everyday-life example of a technology that could not work without humans mastering QM in analogy to the application of GR in GPS? The GPS is a very handy example in explaining to a broad audience why it is useful for humanity to know the laws of general relativity. It nicely bridges the abstract theory with daily life technologies! I'd like to know an analogous example of a technology which could not have been developed by engineers who didn't understand the rules of quantum mechanics. (I guess that I should say quantum mechanics, because asking for a particle physics application could be too early.) To bound the question: No future applications (e.g. teleportation). No uncommon ones (for, who has a quantum computer at home?). A less frequently-cited example than the laser, please. If possible, for sake of simplicity, we'll allow that the quantum theory appears in form of a small correction to the classical one (just like one doesn't need the full apparatus of general relativity to deduce the gravitational red-shift). | Quantum mechanics and everyday nature Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple. | How are quantum gates realised, in terms of the dynamic? When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions. In some sense, these are rather mysterious objects, in that they perform "magic" discrete operations on the states. They are essentially black boxes, whose inner workings are not often dealt with while studying quantum algorithms. However, that is not how quantum mechanics works: states evolve in a continuous fashion following Schrödinger's equation. In other words, when talking about quantum gates and operations, one neglects the dynamic (that is, the Hamiltonian) realising said evolution, which is how the gates are actually implemented in experimental architectures. One method is to decompose the gate in terms of elementary (in a given experimental architecture) ones. Is this the only way? What about such "elementary" gates? How are the dynamics implementing those typically found? | eng_Latn | 4,085 |
How close are we in achieving computation over reals using quantum qubits? I recently attended a seminar where a professor of quantum cryptography told the audience that one quantum qubit can theoretically store "infinite information". I was very intrigued by this statement, and me being an absolute novice in this domain, do not have the means of verifying the validity of his statement. My questions are as follows: Can we really compute the distance $|x - y| < \epsilon$ using a quantum qubit? If so, can anyone throw light on how this is done? Also, if not, how far along are we in actually computing this quantity? Can we measure if quantum computers approximate this quantity better (or worse?) than classical computers? Thanks a lot in advance! | How can infinite information be theoretically encoded or stored in a single qubit? I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a single qubit. I'm not sure I completely comprehend this. Here's how I rationalized it: You take all the information you want to store, put it in binary form, and make it the real component of $\alpha $ or $\beta$ (the coefficients of the computational basis states). Now I'm not sure if I've understood it right, but since it's still fuzzy in my head it would be great to get some kind of ELI5 explanation or possibly a more detailed picture of how this would, even theoretically, be possible. Apologies if the question doesn't meet standards. I'm new to the forum and would be open to feedback regarding asking questions or answering them. | Inexact measurement and wavefunction collapse As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is $\psi(q)=\delta(q-q_0)$ where $q_0$ is result of measurement. Now, in reality measurements are never exact, so the wavefunction should not have that sharp peak. Instead it should be broadened depending on precision of measurement. In this case, can we still introduce an operator, an eigenstate of which would the new wavefunction appear? Is it useful in any way? Or does the new wavefunction depend too much on the way it was measured so that each instrument would have its own operator? How would such opeartor look e.g. for a single-slit experiment? | eng_Latn | 4,086 |
Magnets quantum locking/levitating How does cooling a magnet allow it to quantum lock/levitate? I have seen it in videos but do not know how it works. | How does quantum trapping with diamagnets work? I just saw demonstration by someone from a Tel Aviv University lab. What they achieved there is mind blowing. I myself own a levitron that uses the Hall effect to levitate a magnet, the problem with that is the magnet must always be flat facing the Hall effect base, any unbalance will wreck the levitation. But in the case of the video you can see that he isn't constrained by such things, the disk can levitate and stay still at whatever angle and orientation. Instead of being levitated, the disk is simply being held still. How does this happen? He referred to this as quantum trapping, but I've little idea about what that is.... Also, what material is the base in these demos? Is the circular track in the demonstration magnetic? I assume this is so. Is there any conceivable way for this technology to make objects levitate on any surface? | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | eng_Latn | 4,087 |
Is there any tool or simulator for Topological quantum gates and circuits? I am starting to step into the field of Topological Quantum Information and Computation and am in search of tools which I can use to directly simulate or realize these transformations in a textual or graphical manner. | Topological Circuit Simulator Does something like exist for topological (eg. braided) circuits? Alternatively, any ideas on how @ is getting (or something similar)? | What is time dilation really? Please will someone explain what time dilation really is and how it occurs? There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens. | eng_Latn | 4,088 |
Gravitational wave behavior My guestion is since we have now detected gravitational waves can gravitational waves go through interference (ie destructive or constructive interference) with each other like other waves? | What Happens When A Gravitational Wave Interacts With Another One? If two gravitational waves came in contact with each other what would happen? In another question entirely, what happens when a higher gravitational field interacts with a weaker one. | How are quantum gates realised, in terms of the dynamic? When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions. In some sense, these are rather mysterious objects, in that they perform "magic" discrete operations on the states. They are essentially black boxes, whose inner workings are not often dealt with while studying quantum algorithms. However, that is not how quantum mechanics works: states evolve in a continuous fashion following Schrödinger's equation. In other words, when talking about quantum gates and operations, one neglects the dynamic (that is, the Hamiltonian) realising said evolution, which is how the gates are actually implemented in experimental architectures. One method is to decompose the gate in terms of elementary (in a given experimental architecture) ones. Is this the only way? What about such "elementary" gates? How are the dynamics implementing those typically found? | eng_Latn | 4,089 |
Is there any way to see that $H= p^2 +x^2$ has level-spaced spectrum from the symmetry? I heard that Ken Wilson had an explanation of the level-spacing of the harmonic oscillator spectrum directly from the symmetry of $H$ under interchange of $p$ and $x$, without ladder operators or direct computation. After some thought, I don't know what such an explanation may be. | Why are the energy levels of a simple harmonic oscillator equally spaced? The energy level of a simple harmonic oscillator is $E_n=(n+\frac{1}{2})\hbar\omega$. Is there any physical explanation why these levels are equally spaced ($= \hbar\omega$)? Maybe this can be helpful. | What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold? The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice). Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector. If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't. Alice and Bob can be spatially separated... What am I misunderstanding? The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol... There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: | eng_Latn | 4,090 |
Was Q Created in the very first Star Trek Movie? This question is based off the end of the very first Star Trek Movie, so I will ask it in spoilers in the odd case that you haven't seen it yet. At the end of the movie Kirk asked Bones and Spock if they had just witnessed the making/creation of a new species. during the Movie they gathered that the Voyager Satellite/probe had possibly gone through a worm hole that took it to the other side of the universe and possibly through time. So my thoughts are that the merged species disappeared possibly through time. could this theoretically have been the beginning of the Q? | Where did the Q come from, before the Q Continuum? In the Star Trek Universe where did the Q come from? I mean before they were Q in the Q Continuum? In Star Trek Voyager you learn that the race is somewhat intolerant of individualism (in the episode of the Q Civil War) but Q also suggest they have always been Q. Is that statement true, have the Q always been the Q? or were they a race that evolved into omniscience? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,091 |
Confusion regarding fundamental particles As per standard model, particles like electron and quarks are considered as the elementary particles (no further division into simpler particles possible). Are those particles really elementary or people don't have enough resources (theories, instruments, energy) to break them into simpler particles at present? | Why do physicists think that the electron is an elementary particle? When we first discovered the proton and neutron, I'm sure scientists didn't think that it was made up of quark arrangements, but then we figured they could be and experiments proved that they were. So, what is it about the electron that leads us to believe that it isn't a composite particle? What evidence do we have to suggest that it it isn't? | How are qubits better than classical bit if they collapse to a classical state after measurement? Classical computers store information in bits, which can either be $0$ or $1$, but, in a quantum computer, the qubit can store $0$, $1$ or a state that is the superposition of these two states. Now, when we make a "measurement" (to determine the state of qubit), it changes the state of the qubit, collapsing it from its superposition of $0$ and $1$ to the specific state consistent with the measurement result. If from a measurement of a qubit we obtain only a single bit of information ($0$ or $1$, because the qubit collapses to either of the states), then, how is a qubit better than a classical bit? Since ultimately we are only able to get either $0$ or $1$ from either classical or quantum bit. If you can explain with an example, it may be helpful. | eng_Latn | 4,092 |
What if n of RSA is same for two people over the network? I was just going through RSA encryption scheme and was trying to figure out how to do all maths. I was suddenly struck by the question that (e,n) is public to the people. How easy it becomes to attack one's system if you find out that you are using same n as someone else? | Using same modulus for RSA I know that there exist some attack when using same modulus. But with a little modification, $m$ is the plain-text $N$ is the RSA modulus $r_1, r_2$ is the random padding $e, s$ is the public exponent $C_e, C_s$ is the cipher-text encrypt as follow $$С_e = (m + r_1)^e \bmod N$$ $$С_s = (m + r_2)^s \bmod N$$ If attacker only knows $C_e, C_s, r_1, r_2, e, s, N$. Is it possible to know $m$? It seems the does not work? | Understanding quantum entanglement.. help me validate this analogy! I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | eng_Latn | 4,093 |
I don't understand why quantum entanglement seems so surprising to physicists in the case of communication. Let us say we take a pair of shoes, and put the two shoes in two separate boxes, and shoot one of the box into a black hole while holding the other box at the other end of the universe. If I were to open the box inside the black hole and find the left shoe in it, it is obvious that the other shoe in the far end of the universe will be a right shoe. The two objects are pre-entangled pairs, there is no need of further communication to maintain their entanglement. | I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. Both envelopes have this written on them: Hello! Open this letter... If the paper inside is red, then other envelope has blue paper. If the paper inside is blue, then other envelope has red paper. So, if I open one letter, and the paper inside is red, then I know the other letter contains the blue paper. Is this equivalent to quantum entanglement? The fact that I will know the color of the other paper when I open (i.e. observe) one envelope? In theory, if one of the letters "appeared" in a different galaxy, I would still know the color of the paper inside that letter, just by opening my letter, instantly, correct? Before I open the letter, is the paper inside each envelope in superposition (??), i.e. 50/50, red or blue? In this analogy, I am assuming that what's written on the letters is true. Is this a correct assumption in quantum physics? I think so yes? In real quantum physics, would I be able to change the color of one paper, so that I change the color of the other one? No right? | How do we show that equality holds in the triangle inequality $|a+b|=|a|+|b|$ iff both numbers are positive, both are negative or one is zero? I already showed that equality holds when one of the three conditions happens. | eng_Latn | 4,094 |
I was wondering, whether there are any problems that we already know are difficult to solve for a quantum computer, and that we could potentially use in cryptography, just as we do now with e.g. the factorization of integers? | Quantum computers are known to be able to crack a broad range of cryptographic algorithms which were previously thought to be solvable only by resources increasing exponentially with the bit size of the key. An example for that is . But, as far I know, not all problems fall into this category. On , we can read Researchers have developed a computer algorithm that doesn’t solve problems but instead creates them for the purpose of evaluating quantum computers. Can we still expect a new cryptographic algorithm which will be hard to crack using even a quantum computer? For clarity: the question refers to specifically to the design of new algorithms. | It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks. One of the most commonly cited examples of a problem in which quantum computers would outperform classical devices is $\text{Factoring}$, but then again, it is also not known whether $\text{Factoring}$ is also efficiently solvable with a classical computer (that is, whether $\text{Factoring}\in \text{P}$). For other commonly cited problems in which quantum computers are known to provide an advantage, such as database search, the speedup is only polynomial. Are there known instances of problems in which it can be shown (either proved or proved under strong computational complexity assumptions) that quantum computers would provide an exponential advantage? | eng_Latn | 4,095 |
In particle in square potential barrier problem, we can easily find that some probabilities exist which express how many particles can go beyond of the potential wall. So my question is that, can we find some particles in the potential wall - square of wave function's norm really means probability of find a particle in the wall? | I understand that if a particle approaches a finite potential barrier of height $V_0$ with energy $E < V_0$, there is still a finite probability of finding the particle on the other side of the barrier due to quantum tunneling. My question is, since the wavefunction is nonzero inside the barrier region, is it possible to actually make a position measurement and locate a particle inside the barrier? I mean, if we can say that "there is a nonzero probability that the particle is inside the barrier", surely this would suggest we can do so? If not, why not? Am I understanding the whole wavefunction/probability distribution thing right? | Why massless particles have zero chemical potential? | eng_Latn | 4,096 |
I realized that Quantum Random Access Memory (qRAM) was proposed to make quantum computers more similar to classical one. Currently quantum computers have very constrained memory, given only quantum registers on quantum processors can be used for an algorithm to run. It is true that e.g. Qiskit language allows to use RAM or HDD of classical computer, however, resulting algorithms are hybrid quantum-classical. I found some proposals how to implement qRAM, e.g. . But my understanding is that the device is highly experimental nowadays. So my questions are those: Does anybody know about progress in this field? Some links to articles of state-of-art implementation of qRAM will be highly appreciated. What about IBM Q? Do we have an opportunity to use qRAM on IBM Q computer in foreseeable future (i.e. few years)? | Presently, how much information can a quantum computer store, in how many qubits? What restrictions are there and how does it vary across realizations (efficiency of data storage, ease of reading and writing, etc)? | I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons. How can I recover my account? (This Q&A is meant as a general description for all Google and Gmail username/password questions. See: ) | eng_Latn | 4,097 |
I'm a complete newbie to Quantum Theory, but I want to know more, so I've been watching few YouTube videos (an example below). All videos I've watched explain, that when an entangled particle has its spin measured, it will instantaneously communicate its measurement with its entangled partner, so that when it too is measured in the same direction, it will have the opposite spin. Often these videos explain why these particles must be communicating with each other, rather than containing "hidden information" (Bell's theorem), but do not delve into why it must be instant. | I have never found experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed. Using the spin up spin down example we know that one of the particles will be spin up and the other spin down, so when we measure one and find it is spin up we know the other is spin down. Is there any situation after creation that the particle with spin up will change to spin down? | It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect the state of the entangled partner. For example, if Alice and Bob share an entangled pair of electrons and Alice measures her spin in the $x$ direction, then Bob's spin will also end up spinning in that direction, and similarly if she measures in the $z$ direction. Moreover, the effect will be instantaneous, regardless of the spatial distance between the two particles, which seems at odds with special relativity. Can I use a scheme like this to communicate faster than light? | eng_Latn | 4,098 |
I saw a video in which a guy from IBM was explaining (very generally) quantum computing, it's difference with classical computing etc. The talk was not technical at all, it was intended for a broad audience. At some point he told that, if we need to represent our position on the planet with only one bit, we could only tell for example if we are on the North or South hemisphere, but with a qubit we could tell exactly where we where. He did this example to explain the difference in how much information can a bit and a qubit contain and to give a little idea of what a superposition is (I think). Now, my question: From what I know a qubit has more than one state, but when I read it I can only have one or zero, so why this example was made? From what I can understand a qubit can hold more information but I can't read it, so basically it's useless. | I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a single qubit. I'm not sure I completely comprehend this. Here's how I rationalized it: You take all the information you want to store, put it in binary form, and make it the real component of $\alpha $ or $\beta$ (the coefficients of the computational basis states). Now I'm not sure if I've understood it right, but since it's still fuzzy in my head it would be great to get some kind of ELI5 explanation or possibly a more detailed picture of how this would, even theoretically, be possible. Apologies if the question doesn't meet standards. I'm new to the forum and would be open to feedback regarding asking questions or answering them. | Compared to, for example, completing 5 bounties in each of 5 different games. | eng_Latn | 4,099 |
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