An asymptotic property of factorizable completely positive maps and the Connes embedding problem
arXiv:1408.6476 · doi:10.1007/s00220-015-2325-9
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.
29 pages