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Title: Relaxed Bell inequalities with arbitrary measurement dependence for each observer

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 M 1 and M 2 , as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call M 1 ^ and M 2 ^ , 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 demonstrate 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 also argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.

Authors:
 [1];  [2];  [3];  [2];  [4]
+ Show Author Affiliations
  1. Univ. of San Diego, San Diego, CA (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  3. Griffith Univ., Brisbane, QLD (Australia)
  4. Harvey Mudd College, Claremont, CA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Australian Research Council Centre of Excellence
OSTI Identifier:
1614776
Alternate Identifier(s):
OSTI ID: 1491941; OSTI ID: 1611856
Grant/Contract Number:  
SC0012567; PHY-1541160; CE110001027
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 99; Journal Issue: 1; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics; Quantum entanglement; Quantum nonlocality

Citation Formats

Friedman, Andrew S., Guth, Alan H., Hall, Michael J. W., Kaiser, David I., and Gallicchio, Jason. Relaxed Bell inequalities with arbitrary measurement dependence for each observer. United States: N. p., 2019. Web. doi:10.1103/PhysRevA.99.012121.
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Friedman, Andrew S., Guth, Alan H., Hall, Michael J. W., Kaiser, David I., & Gallicchio, Jason. Relaxed Bell inequalities with arbitrary measurement dependence for each observer. United States. https://doi.org/10.1103/PhysRevA.99.012121
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Friedman, Andrew S., Guth, Alan H., Hall, Michael J. W., Kaiser, David I., and Gallicchio, Jason. Thu . "Relaxed Bell inequalities with arbitrary measurement dependence for each observer". United States. https://doi.org/10.1103/PhysRevA.99.012121. https://www.osti.gov/servlets/purl/1614776.
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@article{osti_1614776,
title = {Relaxed Bell inequalities with arbitrary measurement dependence for each observer},
author = {Friedman, Andrew S. and Guth, Alan H. and Hall, Michael J. W. and Kaiser, David I. and Gallicchio, Jason},
abstractNote = {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 demonstrate 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 also argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.},
doi = {10.1103/PhysRevA.99.012121},
journal = {Physical Review A},
number = 1,
volume = 99,
place = {United States},
year = {Thu Jan 24 00:00:00 EST 2019},
month = {Thu Jan 24 00:00:00 EST 2019}
}
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https://doi.org/10.1103/PhysRevA.99.012121
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