RT Journal Article
T1 Connes' embedding problem and Tsirelson's problem
A1 Navascués Cobo, Miguel
A1 Pérez García, David
A1 Junge, Marius
A1 Palazuelos Cabezón, Carlos
A1 Scholz, Volkher
A1 Werner, Reinhard
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 positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem.
PB American Institute of Physics
SN 0022-2488
YR 2011
FD 2011
LK https://hdl.handle.net/20.500.14352/41897
UL https://hdl.handle.net/20.500.14352/41897
LA eng
NO Unión Europea. FP7
NO Comunidad de Madrid
DS Docta Complutense
RD 1 jul 2025