{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:36:57Z","timestamp":1775936217504,"version":"3.50.1"},"reference-count":78,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"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>The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by quantum physics, quantified by the guessing probability, can generally be bounded numerically. However, currently only a few exact analytic solutions are known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell inequality. Here, we study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality. We give tight upper bounds on the guessing probabilities associated with one and two of the parties' measurement outcomes as a function of the Mermin inequality violation. Finally, we discuss the possibility of device-independent secret sharing based on the Mermin inequality and argue that the idea seems unlikely to work.<\/jats:p>","DOI":"10.22331\/q-2018-08-17-82","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T10:05:46Z","timestamp":1534500346000},"page":"82","source":"Crossref","is-referenced-by-count":28,"title":["Randomness versus nonlocality in the Mermin-Bell experiment with three parties"],"prefix":"10.22331","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7696-4461","authenticated-orcid":false,"given":"Erik","family":"Woodhead","sequence":"first","affiliation":[{"name":"ICFO - Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2686-833X","authenticated-orcid":false,"given":"Boris","family":"Bourdoncle","sequence":"additional","affiliation":[{"name":"ICFO - Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1355-3435","authenticated-orcid":false,"given":"Antonio","family":"Ac\u00edn","sequence":"additional","affiliation":[{"name":"ICFO - Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"},{"name":"ICREA - Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, Lluis Companys 23, 08010 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"0","doi-asserted-by":"crossref","unstructured":"J. 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