Connes' embedding problem and Tsirelson's problem

M. Junge, M. Navascues, C. Palazuelos, D. Perez-Garcia, V. B. Scholz, R. F. Werner

Research output: Contribution to journalArticle (Academic Journal)

54 Citations (Scopus)

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.
Original languageEnglish
JournalJournal of Mathematical Physics
DOIs
Publication statusPublished - 6 Aug 2010

Keywords

  • math-ph
  • quant-ph
  • math.MP

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    Junge, M., Navascues, M., Palazuelos, C., Perez-Garcia, D., B. Scholz, V., & F. Werner, R. (2010). Connes' embedding problem and Tsirelson's problem. Journal of Mathematical Physics. https://doi.org/10.1063/1.3514538