TY - JOUR

T1 - Extreme Points and Factorizability for New Classes of Unital Quantum Channels

AU - Haagerup, Uffe

AU - Musat, Magdalena

AU - Ruskai, Mary Beth

N1 - Correction: https://link.springer.com/article/10.1007%2Fs00023-021-01083-8

PY - 2021

Y1 - 2021

N2 - We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family of channels given by completely positive (CP) maps M3(C) ↦ M3(C) which are both unital and trace-preserving. Almost every member of this family is factorizable and extreme in the set of CP maps which are both unital and trace-preserving, but is not extreme in either the set of unital CP maps or the set of trace-preserving CP maps. We also study a large class of maps which generalize the Werner-Holevo channel for d= 3 in the sense that they are defined in terms of partial isometries of rank d- 1. Moreover, we extend this to maps whose Kraus operators have the form t|ej⟩⟨ej|⊕V with V∈ Md-1(C) unitary and t∈ (- 1 , 1). We show that almost every map in this class is extreme in both the set of unital CP maps and the set of trace-preserving CP maps. We analyze in detail a particularly interesting family which is extreme unless t=-1d-1. For d= 3 , this includes a pair of channels which have a dual factorization in the sense that they can be obtained by taking the partial trace over different subspaces after using the same unitary conjugation in M3(C) ⊗ M3(C).

AB - We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family of channels given by completely positive (CP) maps M3(C) ↦ M3(C) which are both unital and trace-preserving. Almost every member of this family is factorizable and extreme in the set of CP maps which are both unital and trace-preserving, but is not extreme in either the set of unital CP maps or the set of trace-preserving CP maps. We also study a large class of maps which generalize the Werner-Holevo channel for d= 3 in the sense that they are defined in terms of partial isometries of rank d- 1. Moreover, we extend this to maps whose Kraus operators have the form t|ej⟩⟨ej|⊕V with V∈ Md-1(C) unitary and t∈ (- 1 , 1). We show that almost every map in this class is extreme in both the set of unital CP maps and the set of trace-preserving CP maps. We analyze in detail a particularly interesting family which is extreme unless t=-1d-1. For d= 3 , this includes a pair of channels which have a dual factorization in the sense that they can be obtained by taking the partial trace over different subspaces after using the same unitary conjugation in M3(C) ⊗ M3(C).

UR - http://www.scopus.com/inward/record.url?scp=85107775601&partnerID=8YFLogxK

U2 - 10.1007/s00023-021-01071-y

DO - 10.1007/s00023-021-01071-y

M3 - Journal article

AN - SCOPUS:85107775601

VL - 22

SP - 3455

EP - 3496

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

ER -