Relaxed Bell inequalities and Kochen-Specker theorems

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Title Relaxed Bell inequalities and Kochen-Specker theorems
Author Hall, Michael
Journal Name Physical Review A
Year Published 2011
Place of publication United States
Publisher American Physical Society
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 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.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1103/PhysRevA.84.022102
Copyright Statement Copyright 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.
Volume 84
Issue Number 2
Page from 022102-1
Page to 022102-16
ISSN 1050-2947
Date Accessioned 2011-11-24
Language en_US
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Quantum Information, Computation and Communication; Quantum Physics
URI http://hdl.handle.net/10072/42804
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1x

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