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arXiv · 1408.6476

An asymptotic property of factorizable completely positive maps and the Connes embedding problem

Uffe Haagerup·Magdalena Musat
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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.

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Uffe Haagerup, Magdalena Musat. 2014-08-27. An asymptotic property of factorizable completely positive maps and the Connes embedding problem. https://doi.org/10.1007/s00220-015-2325-9

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