Relaxed Bell inequalities with arbitrary measurement dependence for each observer
Name
PhysRevA.99.012121.pdf
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1.7 MB
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Adobe PDF
Checksum (MD5)
37754c700b021133f600c4708a937079
Author(s)
Friedman, Andrew S.
Hall, Michael J. W.
Gallicchio, Jason
Guth, Alan
Kaiser, David I
Date Issued
January 2019
Journal
Physical Review A
Publisher
American Physical Society
Citation
Friedman, Andrew S. et al. “Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer.” Physical Review A 99, 1 (January 2019): 012121 © 2019 American Physical Society
Version
Final published version
Abstract
Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as "measurement independence" (also referred to as "freedom of choice" or "settings independence"). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence for each observer using the parameters M1 and M2, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call M1 and M2, deriving a modified Bell inequality for each description. These "relaxed" inequalities subsume those considered in previous work as special cases, and quantify how much the assumption of measurement independence needs to be relaxed in order for a locally causal model to produce a given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We show that both relaxed Bell inequalities are tight bounds on the CHSH parameter by constructing locally causal models that saturate them. For any given Bell inequality violation, the new two-parameter and four-parameter models each require significantly less mutual information between the hidden variables and measurement settings than previous models. We conjecture that the new models, with optimal parameters, require the minimum possible mutual information for a given Bell violation. We further argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.99.012121
