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  • Correlation Distance and Bounds for Mutual Information

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    89572_1.pdf (256.1Kb)
    Author(s)
    Hall, Michael JW
    Griffith University Author(s)
    Hall, Michael J.
    Year published
    2013
    Metadata
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    Abstract
    The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information between pairs of two-valued classical variables and quantum qubits, in terms of the corresponding classical and quantum correlation distances. These bounds are stronger than the Pinsker inequality (and refinements thereof) for relative entropy. The classical lower bound may be used to quantify properties of statistical models that violate Bell inequalities. Partially entangled qubits can have ...
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    The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information between pairs of two-valued classical variables and quantum qubits, in terms of the corresponding classical and quantum correlation distances. These bounds are stronger than the Pinsker inequality (and refinements thereof) for relative entropy. The classical lower bound may be used to quantify properties of statistical models that violate Bell inequalities. Partially entangled qubits can have lower mutual information than can any two-valued classical variables having the same correlation distance. The qubit correlation distance also provides a direct entanglement criterion, related to the spin covariance matrix. Connections of results with classically-correlated quantum states are briefly discussed.
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    Journal Title
    Entropy
    Volume
    15
    DOI
    https://doi.org/10.3390/e15093698
    Copyright Statement
    © 2013 by the author; licensee MDPI, author. This is an Open Access article distributed under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
    Subject
    Mathematical sciences
    Physical sciences
    Quantum information, computation and communication
    Publication URI
    http://hdl.handle.net/10072/56160
    Collection
    • Journal articles

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