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 Wn- are factorizable, for all odd integers n different from 3. Furthermore, we investigate factorizability of convex combinations of W3+ and W3-, a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.
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