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 |
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dc.relation.ispartofseries |
Journal of Mathematical Physics 52 (2011), Nr. 1 |
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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 |
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dc.relation.essn |
1089-7658 |
|
dc.relation.issn |
0022-2488 |
|
dc.relation.doi |
https://doi.org/10.1063/1.3514538 |
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dc.bibliographicCitation.issue |
1 |
|
dc.bibliographicCitation.volume |
52 |
|
dc.bibliographicCitation.firstPage |
12102 |
|
dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|