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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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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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 ...
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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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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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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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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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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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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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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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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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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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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 ...
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Did anyone claim that quantum theory meant lasers would never work

I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many ...
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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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Why do they call it quantum teleportation?

So I have been trying to learn about entanglement and quantum teleportation and from what I've been able to gather so far, the teleportation part seems to be misleading. At first I thought that the ...
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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 ...
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What are qubits made of in Wen's string-net theory?

In Prof. Xiaogang Wen's theory, photons and electrons are described as quasi-particles appeared as a result of the existence of the string-net liquid, which is the topological order of the qubits that ...
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using a unitary matrix to transpose

A unitary matrix U is a matrix such that the conjugate transpose of U, when multiplied on the right with U, yields identity. My question is, is it possible to obtain the transpose of any density ...
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Fast algorithm for maximizing the quantum fidelity

Consider the following optimization problem: Given a quantum state $\sigma$, a constant $b$ and a Hermitian operator $A$, find $\underset{\rho} \max F(\rho,\sigma)$ subject to $\text{Tr}(\rho ...
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Constructing a CP map with some decaying property

Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
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Can quantum measurement process be thought of as a sieve?

Consider an observable represented by the Hermitian operator $$A=\sum_{a'}a' |a'\rangle \langle a'|.$$ As I read on Sakurai's textbook, the process of measuring $A$ throws a system ...
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Is Tsirelson's Bound the only constraint on these quantum correlations?

Alice and Bob are each in possession of one half of a maximally entangled pair of particles. Alice can make either of two observations, $A_1$ or $A_2$. Bob can make either of two observations, $B_1$ ...
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Double slit experiment where the “particle” is a macroscopic capsule with people inside

I understand that the double slit experiment (i.e. the creation of interference pattern) holds also when the "particle" is not just a single particle but any item, experimentally proven even for a C60 ...
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Why is optical orbital angular momentum (OAM) called “topological charge”?

The terminology "topological charge" is frequent in lots of research papers related to optical vortex or optical OAM, it is used to represent the optical OAM. Why? How to comprehend it?
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Matlab package: graphical calculus for quantum operations (esp. linear optics)

I need a matlab package that will make my life easier. I have quantum circuits with optical beam splitters, polarizing beam splitters and photodetectors. These circuits are getting very complicated ...
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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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Equivalence classes in a Hilbert space

I'm reading something about quantum information/quantum computing theory, and I've run into a wall. I know what is meant by an equivalence class and how something can be partitioned into equivalence ...
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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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Couder-Fort Oil Bath Experiments and Quantum Entanglement Phenomena

The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit ...
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What is the code distance in quantum information theory?

What is the code distance in quantum information theory? Code distance seems to be a very important concept in fault tolerant quantum computation and topological quantum computation.
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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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Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
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Tracing out an observable vs integrating over unitaries

Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define $\displaystyle O_B = ...
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What is the motivation for the definition of concurrence in quantum information?

What is the motivation for the definition of concurrence in quantum information? On the surface, the definition looks pretty ad hoc. The definition is often given for the case of 2 qubits only. What ...
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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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Conservation of energy in quantum teleportation

Consider the quantum state teleportation protocol of Bennett et. al. How does one prove that this protocol would never violate the conservation of energy? At the face of it, it doesn't seem to be ...
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Quantum Error Correction: Surface code vs. color code

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit ...
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SciFi Stasis Field and the Quantum Zeno Effect

The Quantum Zeno Effect concerns the use of repeated measurement of a particle to prevent the time evolution of the wave function, and hence "freeze" it in the observed state. A Stasis Field is a ...
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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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What are the prerequisites to study topological quantum computation/topological phases of the matter? [closed]

I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if ...
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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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When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
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Is it possible to use quantum mechanics for an effective time based encryption?

This is for an application in cryptography. There is a concept called "time based cryptography", where a message can be decrypted only after a certain time, Say "12/12/2060, 12:30 GMT". There are some ...
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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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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 ...