Relaxed Bell inequalities with arbitrary measurement dependence for each observer<\/a><\/p>\n\n\n\nPhysical Review A 99, 012121 (2019)<\/p>\n\n\n\n
Abstract<\/h2>\n\n\n\n
Bell’s inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local \u201chidden variables\u201d that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as \u201cmeasurement independence\u201d (also referred to as \u201cfreedom of choice\u201d or \u201csettings independence\u201d). 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 1 and 2, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call \u02c6 1 and \u02c6 2, deriving a modified Bell inequality for each description. These \u201crelaxed\u201d 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.<\/p>\n","protected":false},"excerpt":{"rendered":"
Andrew S. Friedman, Alan H. Guth, Michael J.W. Hall, David I. Kaiser, and Jason Gallicchio* Relaxed Bell inequalities with arbitrary […]<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","publication_author":[16],"class_list":["post-6451","physics_publications","type-physics_publications","status-publish","hentry","publication_author-gallicchio"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/physics_publications\/6451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/physics_publications"}],"about":[{"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/types\/physics_publications"}],"author":[{"embeddable":true,"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/media?parent=6451"}],"wp:term":[{"taxonomy":"publication_author","embeddable":true,"href":"https:\/\/www.hmc.edu\/physics\/wp-json\/wp\/v2\/publication_author?post=6451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}