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    Probabilistic inequalities and measurements in bipartite systems

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    Vourdas_Jnl_of_Physics_A.pdf (331.6Kb)
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    Publication date
    2019-01
    Author
    Vourdas, Apostolos
    Keyword
    Probabilistic inequalities
    Quantum states
    Bipartite systems
    Boole inequalities
    CHSH inequalities
    Rights
    This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aafe97.
    Peer-Reviewed
    Yes
    
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    Abstract
    Various inequalities (Boole inequality, Chung–Erdös inequality, Frechet inequality) for Kolmogorov (classical) probabilities are considered. Quantum counterparts of these inequalities are introduced, which have an extra 'quantum correction' term, and which hold for all quantum states. When certain sufficient conditions are satisfied, the quantum correction term is zero, and the classical version of these inequalities holds for all states. But in general, the classical version of these inequalities is violated by some of the quantum states. For example in bipartite systems, classical Boole inequalities hold for all rank one (factorizable) states, and are violated by some rank two (entangled) states. A logical approach to CHSH inequalities (which are related to the Frechet inequalities), is studied in this context. It is shown that CHSH inequalities hold for all rank one (factorizable) states, and are violated by some rank two (entangled) states. The reduction of the rank of a pure state by a quantum measurement with both orthogonal and coherent projectors, is studied. Bounds for the average rank reduction are given.
    URI
    http://hdl.handle.net/10454/16778
    Version
    Accepted Manuscript
    Citation
    Vourdas A (2019) Probabilistic inequalities and measurements in bipartite systems. Journal of Physics A: Mathematical and Theoretical. 52(8): 085301.
    Link to publisher’s version
    https://doi.org/10.1088/1751-8121/aafe97
    Type
    Article
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    Engineering and Informatics Publications

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