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

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.

arXiv comment29 pages

References in corpus (4)

• Entanglement Measures under Symmetry
• Entanglement of assistance and multipartite state distillation
• Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
• Factorization and dilation problems for completely positive maps on von Neumann algebras

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