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dc.contributor.authorVourdas, Apostolos*
dc.date.accessioned2019-02-01T15:08:37Z
dc.date.available2019-02-01T15:08:37Z
dc.date.issued2019-01
dc.identifier.citationVourdas A (2019) Probabilistic inequalities and measurements in bipartite systems. Journal of Physics A: Mathematical and Theoretical. 52(8): 085301.en_US
dc.identifier.urihttp://hdl.handle.net/10454/16778
dc.descriptionYesen_US
dc.description.abstractVarious 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.en_US
dc.language.isoenen_US
dc.rightsThis 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.en_US
dc.subjectProbabilistic inequalitiesen_US
dc.subjectQuantum statesen_US
dc.subjectBipartite systemsen_US
dc.subjectBoole inequalitiesen_US
dc.subjectCHSH inequalitiesen_US
dc.titleProbabilistic inequalities and measurements in bipartite systemsen_US
dc.status.refereedYesen_US
dc.date.Accepted2019-01-15
dc.date.application2019-01-15
dc.typeArticleen_US
dc.type.versionAccepted Manuscripten_US
dc.identifier.doihttps://doi.org/10.1088/1751-8121/aafe97
refterms.dateFOA2019-02-01T15:08:37Z


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