Biblioteca de la Universidad Complutense de Madrid

Connes' embedding problem and Tsirelson's problem

Impacto

Navascués Cobo, Miguel y Pérez García, David y Junge, Marius y Palazuelos Cabezón, Carlos y Scholz, V. B. y R. F. Werner, R. F. (2011) Connes' embedding problem and Tsirelson's problem. Journal of Mathematical Physics, 52 (1). ISSN 0022-2488

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URL Oficial: http://scitation.aip.org/content/aip/journal/jmp/52/1/10.1063/1.3514538



Resumen

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.


Tipo de documento:Artículo
Palabras clave:Física matemática, Teoría cuántica, Quantum Physics, Mathematical Physics
Materias:Ciencias > Física > Física matemática
Ciencias > Física > Teoría de los quanta
Código ID:12154
Depositado:02 Feb 2011 17:14
Última Modificación:03 Dic 2014 09:55

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