{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T12:51:02Z","timestamp":1756385462795},"reference-count":31,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T00:00:00Z","timestamp":1592438400000},"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>We describe a two-player non-local game, with a fixed small number of questions and answers, such that an <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03f5<\/mml:mi><\/mml:math>-close to optimal strategy requires an entangled state of dimension <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>2<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi mathvariant=\"normal\">\u03a9<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>\u03f5<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>8<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:msup><\/mml:math>. Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick \\cite{ji2018three}. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs \\cite{slofstra2019set, dykema2017non, musat2018non} involved representation theoretic machinery for finitely-presented groups and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>C<\/mml:mi><mml:mo>\u2217<\/mml:mo><\/mml:msup><\/mml:math>-algebras.<\/jats:p>","DOI":"10.22331\/q-2020-06-18-282","type":"journal-article","created":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T11:37:00Z","timestamp":1592480220000},"page":"282","source":"Crossref","is-referenced-by-count":17,"title":["A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations"],"prefix":"10.22331","volume":"4","author":[{"given":"Andrea","family":"Coladangelo","sequence":"first","affiliation":[{"name":"Computing and Mathematical Sciences, Caltech"}]}],"member":"9598","published-online":{"date-parts":[[2020,6,18]]},"reference":[{"key":"0","unstructured":"Antonio Ac\u00edn, Serge Massar, and Stefano Pironio. 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