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Connes' embedding problem and Tsirelson's problem



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Navascués Cobo, Miguel and Pérez García, David and Junge, Marius and Palazuelos Cabezón, Carlos and Scholz, V. B. and R. F. Werner, R. F. (2011) Connes' embedding problem and Tsirelson's problem. Journal of Mathematical Physics, 52 (1). ISSN 0022-2488


Official URL: http://scitation.aip.org/content/aip/journal/jmp/52/1/10.1063/1.3514538


We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem.

Item Type:Article
Uncontrolled Keywords:Física matemática, Teoría cuántica, Quantum Physics, Mathematical Physics
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12154
Deposited On:02 Feb 2011 17:14
Last Modified:03 Dec 2014 09:55

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