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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Mathematically challenging areas in Quantum information theory and quantum cryptography

I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
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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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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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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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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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are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is the ...
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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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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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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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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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Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
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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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Is this theory about Universe and information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...
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Tensor product of Hadamard operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle ...
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What's wrong with this faster-than-light gedankenexperiment?

It is common wisdom - and mathematically proven - that quantum entanglement cannot be used to bypass the relativistic speed limit and transfer information faster than light. So there must be something ...
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number of microstates associated with two-level quantum systems

this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory I'm trying to figure the number of simple quantum states (microstates) of ...
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How could a particle be isolated to avoid decoherence?

The question aims to this issue : if there is some technological arrangement (or action) to take over the particle/system in order to keep it in a coherent state, then the field, (force or whatever) ...
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Entanglement of Mixed Quantum State

As per Wikipedia: Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot ...
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Is there a unitary, linear bijection between (1) Maximally Entangled and (2) Factorizable States?

Pretty much as the title says. I am interested in the two particle system, each particle having two dimensional quantum states; naturally if there is a generalisation I'd be interested in that too. ...
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Dimension of separable state

Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$? This is the relevant passage: So far, we have assumed implicitly that the ...
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How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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Extending mixed states to pure state

Let us consider any pure state $|\psi\rangle\in\mathbb{C^n\otimes C^n\otimes C^n}$. Its reduced bipartite density matrix represent a pure state or mixed state depending on whether $|\psi\rangle$ is ...
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Is it possible to make a state tomography of an entangled state only by measurements on subsystems?

As far as I can understand, to make a state tomography of a composite system, a properly selected set of joint measurements should be carried out on the composite system to estimate the density matrix ...
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On Bell inequality and bound entangled states

I have recently seen some presentation slides of Michał Horodecki (slide number 77) in which he discussed the following conjecture. Bound entangled states satisfy all Bell inequalities The ...
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Again about all-win lottery

I suggest the following thought experiment that describes a machine which makes everybody happy. Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal ...
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What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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How many states are there in the observable universe

If we took a single instant and considered all possible states of all energy and matter do we have any bounds on how much that would be? Would that number be related to information?
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Approaches to Fault tolerant quantum computation

What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for ...
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Can entanglement with an inaccessible system be useful?

Quantum phenomena in bipartite pure state systems like teleportation are pretty well understood. What I'm interested in is the following situation: Alice, Bob and Charlie hold some general tripartite ...
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Classical vs qubits: Superposition

Since a quantum information lecture today I have been wondering what does it really mean for a state to be in superposition? Is this something that is answerable? This is what we learnt (or what I ...
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Spatial and polarizing beam splitters in a graphical calculus

Suppose I have four wires, and I tensor product them together $A \otimes B \otimes C \otimes D$ I pass $A \otimes B$ through a spatial beam splitter $Spl: A \otimes B \rightarrow A^\prime \otimes ...
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Representations of Pauli matrices involving outer product of qubit states

Let $| 0 \rangle$ and $| 1 \rangle $ be the states of qubit. Let $\hat{\sigma_x}$, $\hat{\sigma_y}$, $\hat{\sigma_z}$ be Pauli matrices: $$ \hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ ...
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Approximate cloning of a qubit, given multiple starting copies

Suppose I'm given several clones of a qubit in a pure unentangled state. That is to say, I'm given the state $(a \left|0\right\rangle + b \left|1\right\rangle)^{\otimes n}$. My goal is to make $d$ ...
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Does squeezing a vacuum state produces photons?

A squeezed vacuum state is produced by applying a squeezing operator $S$ on the vacuum state $|0 \rangle$: \begin{eqnarray} S | 0 \rangle = \sum_n C_n |n \rangle \end{eqnarray} My question is, from ...
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Can entanglement be explained as a consequence of conservation laws?

This article at NewScientist magazine (subscription required) describes entangling photons by passing them through a half silvered mirror. ...
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Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
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Extending the idea of superdense coding

I was reading through the superdense coding protocol, that lets A convey two classical bits to B by sending one qubit (assuming B sends A a qubit beforehand). So B creates a 2-qubit state and sends ...
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Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
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Physical meaning of the sign basis in quantum mechanics

If we take a hydrogen atom as qubit, let $\lvert0\rangle$ = unexcited state $\lvert1\rangle$ = excited state then what is the meaning of measuring the qubit value in the sign basis? If the atom may ...
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Can the concurrence be calculated in terms of the entanglement of formation?

Can the concurrence be calculated in terms of the entanglement of formation? If I somehow know the entanglement of formation, $E_F$ for two mixed qubits, where \begin{equation} E_F = -x \log x - ...
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A question about the universal quantum cloning machine (UQCM)

In the recent paper Replicating the benefits of Deutschian closed timelike curves without breaking causality, a quantum state cloner based on open timelike curve (OTC) was mentioned. There to clone ...
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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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Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...