Relaxed Bell inequalities with arbitrary measurement dependence for each observer
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 "meas...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Published: |
American Physical Society
2019
|
| Online Access: | http://hdl.handle.net/1721.1/120708 https://orcid.org/0000-0003-3802-5206 https://orcid.org/0000-0002-5054-6744 |
| _version_ | 1811074351012773888 |
|---|---|
| author | Friedman, Andrew S. Hall, Michael J. W. Gallicchio, Jason Guth, Alan Kaiser, David I |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Friedman, Andrew S. Hall, Michael J. W. Gallicchio, Jason Guth, Alan Kaiser, David I |
| author_sort | Friedman, Andrew S. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:47:41Z |
| format | Article |
| id | mit-1721.1/120708 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:47:41Z |
| publishDate | 2019 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1207082022-09-30T16:55:05Z Relaxed Bell inequalities with arbitrary measurement dependence for each observer Friedman, Andrew S. Hall, Michael J. W. Gallicchio, Jason Guth, Alan Kaiser, David I Massachusetts Institute of Technology. Center for Theoretical Physics Guth, Alan Kaiser, David I 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. United States. Department of Energy (Contract DE-SC0012567) 2019-03-04T19:49:47Z 2019-03-04T19:49:47Z 2019-01 2018-09 2019-02-07T14:09:02Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/120708 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 https://orcid.org/0000-0003-3802-5206 https://orcid.org/0000-0002-5054-6744 http://dx.doi.org/10.1103/PhysRevA.99.012121 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Friedman, Andrew S. Hall, Michael J. W. Gallicchio, Jason Guth, Alan Kaiser, David I Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title | Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title_full | Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title_fullStr | Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title_full_unstemmed | Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title_short | Relaxed Bell inequalities with arbitrary measurement dependence for each observer |
| title_sort | relaxed bell inequalities with arbitrary measurement dependence for each observer |
| url | http://hdl.handle.net/1721.1/120708 https://orcid.org/0000-0003-3802-5206 https://orcid.org/0000-0002-5054-6744 |
| work_keys_str_mv | AT friedmanandrews relaxedbellinequalitieswitharbitrarymeasurementdependenceforeachobserver AT hallmichaeljw relaxedbellinequalitieswitharbitrarymeasurementdependenceforeachobserver AT gallicchiojason relaxedbellinequalitieswitharbitrarymeasurementdependenceforeachobserver AT guthalan relaxedbellinequalitieswitharbitrarymeasurementdependenceforeachobserver AT kaiserdavidi relaxedbellinequalitieswitharbitrarymeasurementdependenceforeachobserver |