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A new viewpoint on factorizable maps and connections to the Connes Embedding Problem Rordam, Mikael
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.
Item Metadata
Title |
A new viewpoint on factorizable maps and connections to the Connes Embedding Problem
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-07-19T09:04
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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.
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Extent |
49.0 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Copenhagen
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Series | |
Date Available |
2020-09-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0394297
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International