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arXiv:1412.0518

Complementary correlations and entanglement distribution

Prasenjit Deb

Published Dec 1, 2014• 0 citations
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Abstract

Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show that for a certain class of states quantum correlations revealed through complementary correlations become equal to entanglement and discord. We also provide a necessary and sufficient condition for entanglement distribution with separable Bell diagonal states in terms of complementary correlations.

DOI
10.48550/arxiv.1412.0518

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Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show that for a certain class of states quantum correlations revealed through complementary correlations become equal to entanglement and discord. We also provide a necessary and sufficient condition for entanglement distribution with separable Bell diagonal states in terms of complementary correlations.
Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here, we explore an effective method to identify the entangled Bell diagonal states by means of Pearson correlation, one of the complementary correlations. Then, we extend this method to expose the dynamic behavior of complementary correlations under various kinds of decoherence channels. The sudden death and revival of entanglement can be explained by the idea of Pearson correlation. The threshold that is used to identify entanglement is proposed. Furthermore, we put forward a new method to expound the underlying physical mechanisms for which classical and quantum correlations suffer a sudden change in the decoherence process.
Quantum correlations in composite and separable quantum systems are characterized by non-vanishing quantum discord. We demonstrate the necessary and sufficient conditions for existence of hermitian witness operators for quantum discord, bypassing the problem of non-convexity of the set of all classical states. We propose an example of a linear witness which can detect quantum correlations in large classes of separable bipartite systems. Decomposition of the witness in terms of a small number of locally measurable operators as shown here, paves the way for experimental detection of quantum correlations beyond entanglement.
The distribution of quantum correlations in multipartite systems plays a significant role in several aspects of quantum information theory. While it is well known that these quantum correlations cannot be freely distributed, the way that they are shared in a multipartite system is an open problem even for a small set of qubits. Based on monogamylike relations between entanglement and discord for nnn-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.
Quantum correlation lies at the very heart of almost all of the non-classical phenomena exhibited by quantum systems composed of two or more subsystems. In recent times it has been pointed out that there is a kind of quantum correlation, namely discord, which is more general than entanglement. Some authors have investigated the phenomenon that for certain initial states the quantum correlations as well as the classical correlations exhibit sudden change under simple Markovian noise. We show that this dynamical behavior of the correlations of both types can be explained using the idea of complementary correlations . We also show that though a certain class of mixed entangled states can resist the monotonic decay of quantum correlations, this is not true for all mixed states. Moreover, pure entangled states of two qubits will never exhibit such sudden change.
Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states, going beyond the entanglement-separability paradigm. In this article we discuss the suitability of QD in what concern its possible asymmetry with relation to the bipartition we choose to compute it. We obtain an analytical formula for a symmetrized version of QD (SQD) in Bell-diagonal states. We observe that if correlation is regarded as a shared property, then the SQD could be a convenient quantifier for asymmetric states.
Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord, a measure for quantum correlations beyond entanglement, is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: There exist states with nonzero quantum discord that nevertheless cannot be used for entanglement distribution. As a result, we show that entanglement distribution is not possible with rank-2 separable states. Our work sheds light on the task of entanglement distribution with separable states and reveals a classification of quantum states with respect to their usefulness for this task.