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Coherent information
About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.
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TL;DR: In this article, the authors consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many, and investigate the consequences of storing information in classical or quantum ways.
Abstract: We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.
46 citations
TL;DR: In this paper, the authors give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information.
Abstract: We give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information. The endpoints of this curve are given by the Holevo-Schumacher-Westmoreland capacity formula and the entanglement-assisted capacity, which is the maximum over all input density matrices of the quantum mutual information. The proof we give is based on the Holevo-Schumacher-Westmoreland formula, and also gives a new and simpler proof for the entanglement-assisted capacity formula.
45 citations
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TL;DR: This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels and some insight can be gained into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.
Abstract: This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems $R$ and $Q$, after which $Q$ is subjected to a dynamical evolution given by the superoperator $\superop^{Q}$. Two interesting quantities can be defined for this process: the entanglement fidelity $F_{e}$ and the entropy production $S_{e}$. It turns out that neither of these quantities depends in any way on the system $R$, but only on the initial state and dynamical evolution of $Q$. $F_{e}$ and $S_{e}$ are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.
45 citations
TL;DR: It is proved that, regardless of the protecting Hamiltonian, there exists a perturbed evolution thatnecessitates a final error correcting step for the state of the memory to be read, and depart from the usual Markovian approximation for a thermal bath by concen-trating on models for which part of the evolution can be calculated exactly.
Abstract: The ability to protect quantum information from the effect of noise is one of the majorgoals of quantum information processing. In this article, we study limitations on theasymptotic stability of quantum information stored in passive N-qubit systems. Weconsider the effect of small imperfections in the implementation of the protecting Hamil-tonian in the form of perturbations or weak coupling to a ground state environment.We thus depart from the usual Markovian approximation for a thermal bath by concen-trating on models for which part of the evolution can be calculated exactly. We provethat, regardless of the protecting Hamiltonian, there exists a perturbed evolution thatnecessitates a final error correcting step for the state of the memory to be read. Suchan error correction step is shown to require a finite error threshold, the lack thereofbeing exemplified by the 3D XZ-compass model [1]. We go on to present explicit weakHamiltonian perturbations which destroy the logical information stored in the 2D toriccode in a time O(log(N)).
45 citations
TL;DR: This work shows how it introduces artifacts in quantum process tomography and explains how the resulting estimate of the superoperator may not be completely positive, and goes on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of thesuperoperator eigenvalue spectra.
Abstract: Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.
45 citations