Questions tagged [quantum-information]

Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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93
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9answers
17k views

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 ...
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What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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5answers
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Should it be obvious that independent quantum states are composed by taking the tensor product?

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 ...
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1answer
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Differences between pure/mixed/entangled/separable/superposed states

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 ...
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4answers
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Understanding the Bloch sphere

It is usually said that the points on the surface of the Bloch sphere represent the pure states of a single 2-level quantum system. A pure state being of the form: $$ |\psi\rangle = a |0\rangle+b |1\...
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3answers
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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. ...
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2answers
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Quantum entanglement faster than speed of light?

recently i was watching a video on quantum computing where the narrators describes that quantum entanglement information travels faster than light! Is it really possible for anything to move faster ...
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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 ...
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Quantum information references

I was hoping you guys could recommend reading material on quantum information. I have a good background in quantum mechanics, including in foundational issues, as covered in Ballentine's Quantum ...
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Is there such a thing as “Action at a distance”?

What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than ...
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Is it possible for more than two particles to be entangled in a quantum way?

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 ...
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now, consider the state $...
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Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
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Trouble with operator-sum representation of a quantum operation

I am reading about the operator-sum representation of quantum operations in Nielsen's and Chuang's 10th Anniversary ed of Quantum Computation and Quantum Information (N&C). I have become quite ...
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6answers
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How many bits are needed to simulate the universe?

This is not the same as: How many bytes can the observable universe store? The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the ...
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Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ for a given complex number $\alpha$ and where $|n\rangle$ is a ...
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2answers
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Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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2answers
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These two operators commute…but their eigenvectors aren't all the same. Why?

The Hamiltonian $$H = \left[ \begin{array}{cccc} a & 0 & 0 & -b \\ 0 & 0 & -b & 0\\ 0 & -b & 0 & 0\\ -b & 0 & 0 & -a \end{array} \right] $$ commutes ...
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Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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1answer
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What is the difference between general measurement and projective measurement?

Nielsen and Chuang mention in Quantum Computation and Information that there are two kinds of measurement : general and projective ( and also POVM but that's not what I'm worried about ). General ...
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What can the D-Wave quantum computer do?

The media are reporting the commercially sold 128-bit quantum computer from D-Wave http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n which of course sounds ...
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Maximum theoretical data density

Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue ...
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What is Quantum Mechanics really about? [duplicate]

This question might sound very silly, so I'm sorry if that's the case. I'll try my best to make my point clear here. Before explaining, just to make clear, I'm not confused because of the Math ...
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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, ...
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What happens to the quantum information of a particle and an antiparticle when they annihilate?

I understand that the quantum no-deleting theorem dictates that it's impossible to delete quantum information, so what happens to the quantum information of a particle and an antiparticle when they ...
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How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
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1answer
927 views

How is conditional probability handled in quantum mechanics?

In ordinary probability theory the conditional probability/likelihood is defined in terms of the joint and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
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4answers
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Delayed Choice Quantum Eraser without retrocausality?

After reviewing the more than half dozen questions on the DCQE here, this doesn't seem to have been asked or answered directly - if I've missed this piece in one of the other questions or answers ...
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0answers
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The number of mutually-unbiased bases in dimension $d$

This recent answer points to the concept of a mutually-unbiased pair of bases, which are orthonormal bases $\{e_1,\ldots, e_d\}$ and $\{f_1,\ldots, f_d\}$ of a $d$-dimensional Hilbert space $\mathcal ...
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1answer
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Quantum teleportation and no-communication theorem

According to the Wikipedia article for the No-communication theorem: In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to ...
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2answers
976 views

“Entangled photons never show interference in the total pattern without coincidence count” implies FTL

In my previous question, the most defended objection to the gedankenexperiment was that "Entangled photons never show interference in the total pattern without coincidence count". Here I show another ...
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3answers
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Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)

In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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Do Category Theory and/or Quantum Logic add value in physics?

I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
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What is the actual meaning of the density operator?

I am not able to understand the definition of the density operator. I know that if $V$ is a vector space and if I have $k$ states belonging to this vector space, say $|\psi_{i}\rangle$ for $1\le i\le ...
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6answers
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Why is $\theta \over 2$ used for a Bloch sphere instead of $\theta$?

I'm a beginner in studying quantum info, and I'm a little confused about the representation of a qubit with a Bloch Sphere. Wikipedia says that we can use $$\lvert\Psi\rangle=\cos\frac{\theta}{2} \...
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4answers
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Is the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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2answers
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How to take partial trace?

$L$ is a linear operator acting on hilbert space $V$ of dimension $n$, $L: V \to V$. The trace of a linear operator is defined as sum of diagonal entries of any matrix representation in same input ...
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5answers
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Plants and quantum mechanics!

I have been working on quantum biology and found something interesting that I would like to write an equation for. Scientists have wondered how plants have such a high efficiency in photosynthesis; ...
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1answer
343 views

How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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3answers
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How many bytes can the observable universe store?

Is the number of states in the Universe countable? What framework could be used to answer the question in the title?
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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be in a statistical ensemble of ...
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1answer
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What does spontaneous symmetry breaking have to do with decoherence?

Background The question here by Prof. Wen, and the answers that follow point out that spontaneous symmetry breaking (SSB) has something to do with decoherence if I understand it crudely correctly. ...
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2answers
893 views

Infinite possibilities of you

"The question you are asking appears to be subjective, and is likely to be closed." Challenge . . . ACCEPTED. Okay, here it is. A friend prone to uplifting aphorisms posted on Facebook: "You Are An ...
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1answer
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Recent breakthroughs in quantum computing?

Can anyone explain to me why we have had no major breakthroughs in the theory of quantum computation in the past 15 years? Shor's algorithm set the standard, since then we've had Grover's algorithm ...
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4answers
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What is coherence in quantum mechanics?

What are coherence and quantum entanglement? Does it mean that two particles are the same? I read this in a book called Physics of the Impossible by Michio Kaku. He says that two particles behave in ...
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2answers
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How many Bits are in a Qubit?

How many bits of information can be stored in a qubit? On making a measurement on a qubit, one can catch it in either $|0\rangle$ or $| 1\rangle$. Seems that measurement on a qubit can not reveal more ...
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2answers
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Faster-than-light communication using Alcubierre warp drive metric around a single qubit?

The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
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1answer
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How to write a generic density matrix for multi qubit system

I was reading the paper device independent outlook on quantum mechanics. The author defines a generic two qubit density matrix as $$ \rho=\frac{1}{4}\left( I \otimes I + \vec{r_{\rho}} \cdot \vec{\...
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2answers
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What exactly does No cloning mean, in the context of Quantum Computing?

I am trying to get an intuitive idea of how the No-Cloning theorem affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right> + Q_1 \left| 1 \...
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2answers
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Proving the unitary relation of ensemble decompositions

In my class it was told that ensemble decompositions of a density operator $\rho$ are not unique, but that the ones that exist are related by a unitary operator. I'm trying to prove this, but I get ...

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