An asymptotic property of factorizable completely positive maps and the Connes embedding problem
Operator Algebras
2015-06-22 v1
Abstract
We establish a reformulation of the Connes embedding problem in terms of an asymptotic property of factorizable completely positive maps. We also prove that the Holevo-Werner channels W_n^- are factorizable, for all odd integers n different from 3. Furthermore, we investigate factorizability of convex combinations of W_3^+ and W_3^-, a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.
Keywords
Cite
@article{arxiv.1408.6476,
title = {An asymptotic property of factorizable completely positive maps and the Connes embedding problem},
author = {Uffe Haagerup and Magdalena Musat},
journal= {arXiv preprint arXiv:1408.6476},
year = {2015}
}
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29 pages