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In particular, we provide a new analytical approach to explore this problem in a device-independent framework, where the fidelity bound holds without assumption about the internal working of devices used in the CHSH test. We give an example which pushes the minimum CHSH threshold from<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>\u2248<\/mml:mo><mml:mn>2.0014<\/mml:mn><\/mml:math>to<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>\u2248<\/mml:mo><mml:mn>2.05<\/mml:mn><mml:mo>,<\/mml:mo><\/mml:math>far from the local bound. This is in sharp contrast with the device-dependent (two-qubit) case, where entanglement is one-to-one related to a non-trivial singlet fidelity. We discuss this result in a broad context including device-dependent\/independent state characterizations with various classical resources.<\/jats:p>","DOI":"10.22331\/q-2020-03-23-246","type":"journal-article","created":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T14:03:30Z","timestamp":1584972210000},"page":"246","source":"Crossref","is-referenced-by-count":10,"title":["What is the minimum CHSH score certifying that a state resembles the singlet?"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8775-2624","authenticated-orcid":false,"given":"Xavier","family":"Valcarce","sequence":"first","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8455-020X","authenticated-orcid":false,"given":"Pavel","family":"Sekatski","sequence":"additional","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3087-8757","authenticated-orcid":false,"given":"Davide","family":"Orsucci","sequence":"additional","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enky","family":"Oudot","sequence":"additional","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"},{"name":"D\u00e9partement de Physique Appliqu\u00e9e, Universit\u00e9 de Gen\u00e8ve, 1211 Gen\u00e8ve, Suisse"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Daniel","family":"Bancal","sequence":"additional","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"},{"name":"D\u00e9partement de Physique Appliqu\u00e9e, Universit\u00e9 de Gen\u00e8ve, 1211 Gen\u00e8ve, Suisse"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Sangouard","sequence":"additional","affiliation":[{"name":"Departement Physik, Universit\u00e4t Basel, Klingelbergstra\u00dfe 82, 4056 Basel, Schweiz"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,3,23]]},"reference":[{"key":"0","unstructured":"Jean-Daniel Bancal, Kai Redeker, Pavel Sekatski, Wenjamin Rosenfeld, and Nicolas Sangouard. 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