{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T06:59:04Z","timestamp":1768633144812,"version":"3.49.0"},"reference-count":63,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T00:00:00Z","timestamp":1603843200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><\/mml:math>-value it will give for a physical experiment. Here we show that to obtain a small expected<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><\/mml:math>-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>I<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi>n<\/mml:mi><mml:mi>n<\/mml:mi><mml:mn>22<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>inequalities.We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><\/mml:math>-value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the na\u00efve approach, which may be of independent interest.<\/jats:p>","DOI":"10.22331\/q-2020-10-28-353","type":"journal-article","created":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T12:10:10Z","timestamp":1603887010000},"page":"353","source":"Crossref","is-referenced-by-count":20,"title":["Bell nonlocality with a single shot"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0155-354X","authenticated-orcid":false,"given":"Mateus","family":"Ara\u00fajo","sequence":"first","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4145-7299","authenticated-orcid":false,"given":"Flavien","family":"Hirsch","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1332-3477","authenticated-orcid":false,"given":"Marco T\u00falio","family":"Quintino","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria"},{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"},{"name":"Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,10,28]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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