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

  title={An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem},
  author={Uffe Haagerup and Magdalena Musat},
  journal={Communications in Mathematical Physics},
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. 

Positively factorizable maps

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