Connes' embedding problem and Tsirelson's problem

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Junge, M. et al.: Connes' embedding problem and Tsirelson's problem. In: Journal of Mathematical Physics 52 (2011), Nr. 1, 012102. DOI: https://doi.org/10.1063/1.3514538

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Sum total of downloads: 63




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Abstract: 
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 II1 factor is a subfactor of the ultrapower of the hyperfinite II1 factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positive answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problemWe 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 II1 factor is a subfactor of the ultrapower of the hyperfinite II1 factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positive answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem
License of this version: Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Document Type: article
Publishing status: publishedVersion
Issue Date: 2011
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of United States United States 31 49.21%
2 image of flag of Germany Germany 16 25.40%
3 image of flag of Spain Spain 3 4.76%
4 image of flag of Poland Poland 2 3.17%
5 image of flag of India India 2 3.17%
6 image of flag of No geo information available No geo information available 1 1.59%
7 image of flag of Russian Federation Russian Federation 1 1.59%
8 image of flag of Japan Japan 1 1.59%
9 image of flag of Israel Israel 1 1.59%
10 image of flag of Austria Austria 1 1.59%
    other countries 4 6.35%

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