Connes' embedding problem and Tsirelson's problem

Show simple item record

dc.identifier.uri http://dx.doi.org/10.15488/8787
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/8840
dc.contributor.author Junge, M.
dc.contributor.author Navascues, M.
dc.contributor.author Palazuelos, C.
dc.contributor.author Perez-Garcia, D.
dc.contributor.author Scholz, V. B.
dc.contributor.author Werner, R.F.
dc.date.accessioned 2019-12-11T12:50:55Z
dc.date.available 2019-12-11T12:50:55Z
dc.date.issued 2011
dc.identifier.citation Junge, M. et al.: Connes' embedding problem and Tsirelson's problem. In: Journal of Mathematical Physics 52 (2011), Nr. 1, 012102. DOI: https://doi.org/10.1063/1.3514538
dc.description.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 II1 factor is a subfactor of the ultrapower of the hyperfinite II1 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' problemWe 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 II1 factor is a subfactor of the ultrapower of the hyperfinite II1 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 eng
dc.language.iso eng
dc.publisher College Park, MD : American Institute of Physics
dc.relation.ispartofseries Journal of Mathematical Physics 52 (2011), Nr. 1
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
dc.subject quantum mechanics eng
dc.subject Hilbert space eng
dc.subject Tsirelson eng
dc.subject.ddc 530 | Physik ger
dc.title Connes' embedding problem and Tsirelson's problem eng
dc.type article
dc.type Text
dc.relation.essn 1089-7658
dc.relation.issn 0022-2488
dc.relation.doi https://doi.org/10.1063/1.3514538
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 52
dc.bibliographicCitation.firstPage 12102
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


Files in this item

This item appears in the following Collection(s):

Show simple item record

 

Search the repository


Browse

My Account

Usage Statistics