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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Kraus operator rank

All quantum operations $\mathcal{E}$ on a system of Hilbert space dimension $\mathcal{d}$ can be generated by an operator-sum representation containing at most $\mathcal{d^2}$ elements. Extending ...
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Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
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Quantum and classical scaling of memory

In the literature of Quantum Computation (QC), when discussing the simulation of quantum systems, one usually comes across comparisons with the classical digital analog such as: "Classically the size ...
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Is there a handwavy way to explain what quantum correlation means?

Is there a simple way to explain the difference between a classical and truly quantum correlation to a non-quantum person who has basic understanding classical correlation? I mean without invoking ...
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Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
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What is the current big question or motivation in quantum information? [closed]

As an prospective student, I am facing a crossing as many people did. I would love to know what is the current big question or motivation in the quantum information society? If anyone knows the answer ...
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What is the difference between maximally entangled and maximally mixed states?

To my understanding, mixed states is composed of various states with their corresponding probabilities, but what is the actual difference between maximally mixed states and maximally entangled states?
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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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What is a completely positive map *physically*?

I am sure this question is really stupid, but I could not refrain from asking it in this forum. This can be considered as a continuation of this question. ...
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If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
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Distinguishability in Quantum Ensembles

Inspired by this question: Are these two quantum systems distinguishable? and discussion therein. Given an ensemble of states, the randomness of a measurement outcome can be due to classical reasons (...
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Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)

In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
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What is quantum discord?

What is quantum discord? I stumbled upon this term on Quantum Computing: The power of discord, but have never heard of it before. Can you give a bit more mathematical explanation of the term here?
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Intuition on positive-operator valued measures (POVM)

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...
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Why are “quadratures” called this way?

In quantum optics (and hence also cv quantum information), given the annihilation and creation operators of the electromagnetic fields $a$ and $a^{\dagger}$, the "position" and "momentum" operators ...
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Quantum Computing and Animal Navigation

Someone sent me this link to a talk by Prof. Klaus Schulten from the University of Illinois: (my emphasis) Quantum Computing and Animal Navigation Quantum computing is all the rage nowadays. ...
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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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Dealing with environment in a CHSH game

I am reading arxiv:1209.0448. I understand that my questions could be highly trivial. I would appreciate if anyone helps me to resolve my confusions. In a CHSH game, Alice and Bob cannot have ...
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Is microcausality *necessary* for no-signaling?

There are proofs in the literature that QFT including microcausality is sufficient for it not to be possible to send signals by making quantum mechanical measurements associated with regions of space-...
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Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...
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Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
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Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle \psi^\dagger(x_2)\psi(x_1)\...
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States diagonal in the tensor product of Bell states.

Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition ...
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Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
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If all the particles of a Bose-Einstein condensate become entangled with each other,does the system still remain a Bose-Einstein condensate?

I know that an entangled system is found in a single entangled state and that when you try to observe the individual state of a particle from an entangled system using a reduced density matrix, you ...
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Indirect probing of entanglement measures

Entanglement is a purely quantum mechanical phenomena that e.q. increase precision of quantum interferometers, atomic clocks or have application in quantum computing. There are many "measures" of ...
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How would a quantum computer receive input from a classical computer?

One of the potential applications of a quantum computer would be as a coprocessor to a classical computing system, much in the same way as a graphics processing unit (GPU) performs specialized ...
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What is discrete phase space?

I've been reading a little about the usual, continuous Wigner functions and phase space quasi-distributions in general, and I believe I understand the idea behind them. The Wigner function arises when ...
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Can quantum vacuum carry entropy?

So, we know that the state of quantum vacuum does carry energy, as it was measured in the Casimir effect. This energy comes from particles almost instantaneous creation and annihilation. Even if they ...
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Why do we want to entangle qubits?

The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
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Does Bekenstein bound imply that the number of possible states of a bounded system is finite?

Bekenstein bound limits the amount of information that can be stored in a system of bounded size and mass. Does that imply that the number of possible states is finite? Does that imply that the number ...
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Quantum Computing Power Advantages

Currently, the world's fastest supercomputer runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some ...
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partial trace with sparse matrices

Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space. For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
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Hayden-Preskill informational mirrors and decryption

I do have a question about an assumption made in the very interesting Hayden-Preskill paper of black holes as informational mirrors. Alice throws her top secret quantum diary which is $k$ qubits long ...
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A 'distance' measure that involves 3 quantum states

The following question was asked by my friend Elie Wolfe. Given two quantum (or even classical) states $\rho, \sigma$, there are various measures that say how 'far' these two quantum states are, such ...
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Group theory and quantum optics

This is a question about application of group theory to physics. The starting point is the group $SU(n)$. I have a representation $R$ of $SU(n)$ that takes values on the unitary group on an infinite ...
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Is there a way to obtain an RG flow equation for Quantum spin systems using MERA

We restrict ourselves to ground states of translationally invariant 1d quantum systems. I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which ...
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Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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A beautiful ion-trap proposal for Boson Sampling: what are its limitations?

A very beautiful recent paper, Scalable Implementation of Boson Sampling with Trapped Ions. C. Shen, Z. Zhang, and L.-M. Duan. Phys. Rev. Lett. 112 no. 5, 050504 (2014); arXiv:1310.4860 ...
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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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Why does quantum cryptography give us uncrackable codes?

Why does quantum cryptography give us uncrackable codes? What makes it 'uncrackable'? Articles in for example pop science magazines always claim QC produces uncrackable coded, however I highly doubt ...
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Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
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Is Interpretation of state vectors and density matrices according to Frequentist or Bayesian interpretation of probability?

I asked a question on math stack exchange what does probability mean. I did not know about Frequentist and Bayesian interpretation of probability previously. So according to which interpretation are ...
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What is the next step beyond quantum computation?

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...
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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 is postselection?

I was reading some questions here. I couldn't understand what it means by postselection. What is postselection? What is its use/significance? Where did it came from?
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Explanation for the power of quantum computers

I have seen various explanations for the power of quantum computers: Quantum computers perform operations in parallel universes Quantum computers can use quantum tunneling to reach a global extremum ...
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Controlled-measurement of a quantum register

Given a state vector $\left[\alpha,\beta,\gamma,\delta\right]$ which is not known a priori, does there exist an operation, which I will call "controlled-measurement", which results in the ensemble $\...
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Information relationship to Special Relativity

How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...