Relaxed Bell inequalities with arbitrary measurement dependence for each observer

Journal Article · Thu Jan 24 00:00:00 EST 2019 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.99.012121· OSTI ID:1614776

Friedman, Andrew S. ^[1]; Guth, Alan H. ^[2]; Hall, Michael J. W. ^[3]; Kaiser, David I. ^[2]; Gallicchio, Jason ^[4]

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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)

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 $\widehat{M_1}$ and $\widehat{M_2}$, 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.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Australian Research Council Centre of Excellence
• Grant/Contract Number: SC0012567; PHY-1541160; CE110001027
• OSTI ID: 1614776
• Alternate ID(s): OSTI ID: 1491941; OSTI ID: 1611856
• Journal Information: Physical Review A, Vol. 99, Issue 1; ISSN 2469-9926
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Optics
Physics
Quantum entanglement
Quantum nonlocality