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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 paper, the authors exploit the modularity of this paradigm to give several concrete extractor constructions, which, e.g., extract all the conditional min-entropy of the source using a seed of length poly-logarithmic in the input, or only require the seed to be weakly random.
Abstract: Randomness extraction involves the processing of purely classical information and is therefore usually studied in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for applications, where side information about the values taken by classical random variables may be represented by the state of a quantum system. This is particularly relevant in the context of cryptography, where an adversary may make use of quantum devices. Here, we show that the well known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information.
We exploit the modularity of this paradigm to give several concrete extractor constructions, which, e.g, extract all the conditional (smooth) min-entropy of the source using a seed of length poly-logarithmic in the input, or only require the seed to be weakly random.
34 citations
TL;DR: In this article, it was shown that the information in a quantum signal source can be extracted in classical form by a measurement leaving the quantum system with less entropy than it had before, but retaining the ability to regenerate the source state exactly from the classical measurement result and the after-measurement state of the system.
Abstract: We inquire under what conditions some of the information in a quantum signal source, namely a set of pure states ψa emitted with probabilities p a, can be extracted in classical form by a measurement leaving the quantum system with less entropy than it had before, but retaining the ability to regenerate the source state exactly from the classical measurement result and the after-measurement state of the quantum system. We show that this can be done if and only if the source states ψa fall into two or more mutually orthogonal subsets.
34 citations
TL;DR: Interpreting the upper bound on the distillable entanglement of a mixed state under one-way and two-way local operations and classical communication (LOCC) as a convex roof extension, it is shown that it reduces to a particularly simple, non-convex optimization problem for the classes of isotropic states and Werner states.
Abstract: We derive general upper bounds on the distillable entanglement of a mixed state under one-way and two-way LOCC. In both cases, the upper bound is based on a convex decomposition of the state into 'useful' and 'useless' quantum states. By 'useful', we mean a state whose distillable entanglement is non-negative and equal to its coherent information (and thus given by a single-letter, tractable formula). On the other hand, 'useless' states are undistillable, i.e., their distillable entanglement is zero. We prove that in both settings the distillable entanglement is convex on such decompositions. Hence, an upper bound on the distillable entanglement is obtained from the contributions of the useful states alone, being equal to the convex combination of their coherent informations. Optimizing over all such decompositions of the input state yields our upper bound. The useful and useless states are given by degradable and antidegradable states in the one-way LOCC setting, and by maximally correlated and PPT states in the two-way LOCC setting, respectively. We also illustrate how our method can be extended to quantum channels.
Interpreting our upper bound as a convex roof extension, we show that it reduces to a particularly simple, non-convex optimization problem for the classes of isotropic states and Werner states. In the one-way LOCC setting, this non-convex optimization yields an upper bound on the quantum capacity of the qubit depolarizing channel that is strictly tighter than previously known bounds for large values of the depolarizing parameter. In the two-way LOCC setting, the non-convex optimization achieves the PPT-relative entropy of entanglement for both isotropic and Werner states.
34 citations
TL;DR: The basics of classical algorithmic complexity theory and two quantum extensions that have been prompted by the foreseeable existence of quantum computing devices are reviewed and the relations between them and the von Neumann entropy rate of generic quantum information sources of ergodic type are examined.
Abstract: We review the basics of classical algorithmic complexity theory and two of its quantum extensions that have been prompted by the foreseeable existence of quantum computing devices. In particular, we will examine the relations between these extensions and the von Neumann entropy rate of generic quantum information sources of ergodic type.
34 citations
TL;DR: In this article, the authors studied the properties of quantum mutual information and coherent information in the infinite-dimensional case, and their properties were studied in detail, and an upper bound for the coherent information was obtained.
Abstract: The paper is devoted to the study of quantum mutual information and coherent information, two important characteristics of a quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given, and their properties are studied in detail. Basic identities relating the quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of the quantum mutual information and coherent information, following from the above identities, is observed. An upper bound for the coherent information is obtained.
34 citations