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

TY - JOUR

T1 - An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem

AU - Haagerup, Uffe

AU - Musat, Magdalena Elena

PY - 2015/9/29

Y1 - 2015/9/29

N2 - 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 (Formula Presented.) are factorizable, for all odd integers n≠3. Furthermore, we investigate factorizability of convex combinations of (Formula Presented.), a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.

AB - 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 (Formula Presented.) are factorizable, for all odd integers n≠3. Furthermore, we investigate factorizability of convex combinations of (Formula Presented.), a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.

U2 - 10.1007/s00220-015-2325-9

DO - 10.1007/s00220-015-2325-9

M3 - Journal article

SN - 0010-3616

VL - 338

SP - 721

EP - 752

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -