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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Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above ...
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Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
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Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
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Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
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Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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How to write a noisy state as a separable operator

Bipartite operators close enough to the identity are separable. But how does one compute the product operator terms of the separable expansion? In particular, if $\left| \Phi \right> = m^{-1/2} ...
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Theoretical or experimental violations of the 2nd Law of Thermodynamics? [closed]

Theoretical challenges to the 2nd Law? What are some the theoretical challenges to the 2nd Law? (cf. Čápek, Vladislav, and Daniel P. Sheehan. Challenges to the Second Law of Thermodynamics: Theory ...
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Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
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Question on quantum computation, entanglement and speed of information propagation

Imagine a following thought experiment. Suppose we have a large amount of entangled particle pairs, several million or billion. Now suppose there are two observers, each carrying one member of ...
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How to obtain stabilizer's generators of a QEC code

The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators. To understand better what I am concerning about, let's consider the 7-qubit ...
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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 state ...
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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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Why is Quantum Teleportation important in Cryptography?

I think the physical principle is that (Wikipedia): For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete ...
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Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( ...
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Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally recorded branches”?

I came across an unusual multi-partite generalization of the Schmidt decomposition in my work, which I describe below. Usually, when people say "a multi-partite Schmidt decomposition", they mean a ...
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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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process matrix - physical interpretation

I have a (probably) advanced question, concerning quantum process tomography. Let's say I have made a measurement with a single qubit, and calculated a $\chi$-matrix which looks like ...
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Local decoherence and entropy

Consider a quantum system consisting of two subsystems, $A$ and $B$. Let $\rho$ be the density matrix of the whole system $A\cup B$. Let $|\alpha\rangle$, $\alpha = 1,2\cdots d_B$, be the states of ...
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Is there any problem a quantum finite state machine can do faster than a classical finite state machine?

All of the quantum algorithms I've seen so far require a turing-complete quantum computer, at least as far as I can tell. Are there any quantum algorithms that require only a quantum finite automaton? ...
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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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A machine which copies any object with 100% accuracy?

Does physics allow for a machine that copies an object with 100% accuracy?
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Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system ...
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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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CHSH Inequality: why $\pi/8$?

I understand the mechanism how CHSH Inequality works. One thing bugs me is why $\pi/8$. I can also take $\pi/100$ for example and $\cos^2(\pi/100)> \cos^2(\pi/8)$ so much better probability and ...
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55 views

Sinusoidaly Driven Two-Level System (TLS)

I'm trying to solve the driven Two-Level System (TLS or qubit) question using a Fourier transform of the Schrodinger equation (SHE), but I'm getting stuck on solving the equation. Given Hamiltonian ...
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No-cloning theorem with 3 particles

I know how to demonstrate that it is not possible to make a unitary operator so that $|a\rangle|0\rangle$ turns into $|a\rangle|a\rangle$ , but is it possible to have $|a\rangle|0\rangle|0\rangle ...
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What is known about the trace of two copies of a channel / four copies of an isometry

Let $\mathcal{E} : \mathcal{L}(A) \to \mathcal{L}(B)$ be a completely positive trace preserving map. By the Choi–Jamiołkowski isomorphism there is an isometry $J : A \to B \otimes C$ such that ...
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What are some examples of infinite state quantum mechanical systems that do not involve free particles?

That is, the quanta are in bound states where there are least upper bounds and greatest lower bounds to their energy states but there are at least a countably infinite many energy levels they can ...
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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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Adiabatic quantum Hamiltonian of variable dimension

Is adiabatic quantum Hamiltonian of variable dimension possible? This is very hypothetical and I am afraid may not have enough merit to belong to this forum. I would still like to elaborate. Here is ...
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Help on applying a Hadamard gate and CNOT to two single q-bits

I am stuck on a few issues in this video. (Note: It is at the frame concerning this question.) In it, from what I understand (which could be wrong) we first apply the Hadamard gate to a qbit in the ...
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How to measure the arbitrariness of a quantum state?

An arbitrary qubit is represented as $\alpha|0\rangle+\beta|1\rangle$ with $|\alpha|^2+|\beta|^2=1$. If we know either $\alpha$ or $\beta$, the state can be completely identified. The 'arbitrariness' ...
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Intuition behind Hamiltonian

I am reading this paper by Das et al. which converts Deutsch's algorithm into an adiabatic quantum algorithm. I don't get the intuition behind the initial and final Hamiltonians. If defines the ...
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Topological quantum computation: abelian vs. non-abelian anyons

We need non-abelian fractional hall states because of the ground state degeneracy http://rmp.aps.org/abstract/RMP/v80/i3/p1083_1 (arXiv version for free). But we can also have degeneracy even in case ...
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Quantum annealing computing

What is Quantum Annealing and quantum annealing computing and what are its advantages and disadvantages with respect to quantum circuit quantum computing/computers?
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Canonical form of GHZ and W state

What is the Schmidt decomposition of the tripartite states$|GHZ\rangle=\frac{1}{\sqrt 2}[|000\rangle+|111\rangle]$ or $|W\rangle=\frac{1}{\sqrt 3}[|001\rangle+|010\rangle+|100\rangle]$? Are these same ...
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Qubit (Qdit) equivalence with bits/bytes/Kbytes/

What is the conversion factor for qubits (qudits) to bits/bytes in classical information theory/computation theory? I mean, how can we know how many "bits/bytes" process, e.g., a 60 qubit quantum ...
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What is the energy scale of a Hamiltonian?

On the second page of this paper a term 'fundamental energy scale' is used while talking about a Hamiltonian. The context is implementing Deutsch's algorithm using Adiabatic Quantum Computation. What ...
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Definition of a 'tunneling lifetime'

I'm given a one-dimensional potential with two wells, one local minimum at some higher energy and one deep global minimum next to it, separated by a barrier of own shape and height (phase qubit). I ...
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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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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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Invariance of states under local unitary transformations [closed]

How can I show explicitly that the bell state $$|\psi^{-}>=\frac{1}{\sqrt{2}}(|0>|1>-|1>|0>)$$ is invariant under local unitary transformations $U_{1}\otimes U_{2}$ ?
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Can Werner states have bound entanglement?

Let us consider the maximally entangled state \begin{equation} |\psi\rangle=\frac{1}{\sqrt{n}}(|0,0\rangle+\cdots+|n-1,n-1\rangle) \end{equation} and construct the pseudo-pure state \begin{equation} ...
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Can the entangelement of basis vectors increase under local operations?

Say I have a bipartite state $\rho = \sum_ip_i|\psi_{i}\rangle \langle \psi_{i}|_{AB}$ Where $\{|\psi_{i}\rangle_{AB}\}$ forms an orthonormal basis. I now perform some local quantum operation on ...
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Do the states forming an orthonormal basis have the same amount of entanglement?

If $\{|\psi_{i}\rangle\}$ is an orthonormal basis for a bipartite system, will $E(|\psi_i\rangle) = E(|\psi_j\rangle)$ for all $i, j$, where $E$ is some entanglement measure?
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Spin Transition Energies

I am reading a paper: http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf On p. 22, the following Hamiltonian is given: $$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + ...
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Question about entangled states

I have a question about entangled state. Suppose I consider the entangled state $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$. I saw an argument for how measurement of the first bit is affected by ...
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Limits of superdense coding

Holevo's theorem says that no more than n bits can be stored (and retrieved) in n qubits. Indeed, allowing error can't improve this either -- the probability of retrieving the correct information is ...
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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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Why does this state have a Schmidt rank of 1?

A system is entangled if and only if the Schmidt rank is greater than 1. Why does this ...