Details
| Original language | Undefined/Unknown |
|---|---|
| Pages (from-to) | 012102 |
| Number of pages | 1 |
| Journal | J. Math. Phys. |
| Volume | 52 |
| Issue number | 1 |
| Publication status | Published - 2011 |
Abstract
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In: J. Math. Phys., Vol. 52, No. 1, 2011, p. 012102.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Connes' embedding problem and Tsirelson's problem
AU - Junge, M.
AU - Navascues, M.
AU - Palazuelos, C.
AU - Perez-Garcia, D.
AU - Scholz, V. B.
AU - Werner, R. F.
N1 - Funding information: This work was supported in part by Spanish grants I-MATH, MTM2008-01366, S2009/ESP-1594, the European projects QUEVADIS and CORNER, DFG grant We1240/12-1 and National Science Foundation grant DMS-0901457. VBS would like to thank Fabian Furrer for stimulating discussions.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
U2 - 10.1063/1.3514538
DO - 10.1063/1.3514538
M3 - Article
VL - 52
SP - 012102
JO - J. Math. Phys.
JF - J. Math. Phys.
SN - 1089-7658
IS - 1
ER -