Published:
[Erscheinungsort nicht ermittelbar]: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery, 2019
Published in:The Many Faceted Connes Embedding Problem (19w5163) ; (Jan. 2019)
Extent:
1 Online-Ressource (487 MB, 00:48:35:28)
Language:
English
DOI:
10.5446/57942
Identifier:
Origination:
Footnote:
Audiovisuelles Material
Description:
We show that the convex set of factorizable quantum channels which factor through finite dimensional C*-algebras is non-closed in each dimension greater than 11, and that there exist factorizable quantum channels that require an ancilla of type II_1. The proof uses analysis of correlation matrices arising from projections, respectively, unitaries, in tracial von Neumann algebras. In recent work, we relate factorizable quantum channels to traces on a certain free product C*-algebra, via their Choi matrices. This new viewpoint leads to central questions in C*-algebra theory and to yet another formulation of the Connes Embedding Problem