{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:29:51Z","timestamp":1754483391559},"reference-count":33,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T00:00:00Z","timestamp":1603670400000},"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 introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><\/mml:math>in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0<\/mml:mn><mml:mo>&lt;<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>such that to succeed with probability<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mo>\u2212<\/mml:mo><mml:mi>\u03b5<\/mml:mi><\/mml:math>in the game it is necessary to use an entangled state of at least<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">\u03a9<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>\u03b5<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\u2212<\/mml:mo><mml:mi>c<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>qubits, and it is sufficient to use a state of at most<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>\u03b5<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>qubits. The game is based on the coherent state exchange game of Leung et al.\\ (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al.\\ (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of 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 respectively.<\/jats:p>","DOI":"10.22331\/q-2020-10-26-349","type":"journal-article","created":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T10:54:35Z","timestamp":1603709675000},"page":"349","source":"Crossref","is-referenced-by-count":3,"title":["A three-player coherent state embezzlement game"],"prefix":"10.22331","volume":"4","author":[{"given":"Zhengfeng","family":"Ji","sequence":"first","affiliation":[{"name":"Centre for Quantum Software and Information, University of Technology Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debbie","family":"Leung","sequence":"additional","affiliation":[{"name":"University of Waterloo and the Perimeter Institute, Canada. Email: \\textttwcleung@uwaterloo.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Vidick","sequence":"additional","affiliation":[{"name":"California Institute of Technology, USA. Email: \\textttvidick@cms.caltech.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,10,26]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"P. Aravind. Quantum mysteries revisited again. American Journal of Physics, 72(10):1303\u20131307, 2004.","DOI":"10.1119\/1.1773173"},{"key":"1","doi-asserted-by":"publisher","unstructured":"A. Aspect, P. Grangier, and G. Roger. Experimental tests of realistic local theories via Bell's theorem. Physical review letters, 47(7):460, 1981.","DOI":"10.1103\/PhysRevLett.47.460"},{"key":"2","doi-asserted-by":"publisher","unstructured":"J. S. Bell. On the Einstein-Podolsky-Rosen paradox. 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