## 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 positive answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem.

Original language | English (US) |
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Article number | 012102 |

Journal | Journal of Mathematical Physics |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Jan 5 2011 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics