Extreme Points and Factorizability for New Classes of Unital Quantum Channels
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Extreme Points and Factorizability for New Classes of Unital Quantum Channels. / Haagerup, Uffe; Musat, Magdalena; Ruskai, Mary Beth.
In: Annales Henri Poincare, Vol. 22, 2021, p. 3455–3496.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 276950059