An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem

By Uffe Haagerup, Magdalena Musat. 2014

59 citations recorded by the source corpus.

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 $${W_n^-}$$Wn- are factorizable, for all odd integers $${n\neq 3}$$n≠3. Furthermore, we investigate factorizability of convex combinations of $${W_3^+}$$W3+ and $${W_3^-}$$W3-, a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/67c673fbb43bfad3f9467525911bf348a4d9a8f1

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In Algebra and Number Theory

1. Gilles Pisier
2. Marius Junge

In Applied Mathematics

1. Gilles Pisier
2. Assaf Naor
3. Benben Liao

In Mathematical Physics

1. Gilles Pisier
2. Marius Junge
3. Assaf Naor
4. Benben Liao
5. Quanhua Xu
6. Javier Parcet
7. Tao Mei

Citations in the corpus

• Tensor Products of C*-Algebras and Operator Spaces (2020, background): “In a different direction, the papers [115, 116] by Haagerup and Musat relate what they call the asymptotic quantum Birkhoff property for factorizable Markov maps to the Connes embedding problem.”