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  • Relaxed Bell inequalities and Kochen-Specker theorems

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    Author(s)
    Hall, Michael JW
    Griffith University Author(s)
    Hall, Michael J.
    Year published
    2011
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    Abstract
    The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong ...
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    The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet-state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various "relaxed" Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen "free will" theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows that existence of an outcome-independent model is equivalent to existence of a deterministic model.
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    Journal Title
    Physical Review A
    Volume
    84
    Issue
    2
    DOI
    https://doi.org/10.1103/PhysRevA.84.022102
    Copyright Statement
    © 2011 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Mathematical sciences
    Physical sciences
    Quantum information, computation and communication
    Quantum physics not elsewhere classified
    Chemical sciences
    Publication URI
    http://hdl.handle.net/10072/42804
    Collection
    • Journal articles

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