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Connes' embedding problem and Tsirelson's problem | | M. Junge
; M. Navascues
; C. Palazuelos
; D. Perez-Garcia
; V. B. Scholz
; R. F. Werner
; | | Date: |
6 Aug 2010 | | 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 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. | | Source: | arXiv, 1008.1142 | | Services: | Forum | Review | PDF | Favorites | |
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