Decomposability of extremal positive unital maps on M₂(ℂ)

Władysław A. Majewski, and Marcin Marciniak. "Decomposability of extremal positive unital maps on M₂(ℂ)." Banach Center Publications 73.1 (2006): 347-356. <http://eudml.org/doc/281593>.

@article{WładysławA2006,
abstract = {A map φ: Mₘ(ℂ) → Mₙ(ℂ) is decomposable if it is of the form φ = φ₁ + φ₂ where φ₁ is a CP map while φ₂ is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map φ: M₂(ℂ) → M₂(ℂ) we construct concrete maps (not necessarily unital) φ₁ and φ₂ which give a decomposition of φ. We also show that in most cases this decomposition is unique.},
author = {Władysław A. Majewski, Marcin Marciniak},
journal = {Banach Center Publications},
keywords = {positive maps; decomposable maps; face structure},
language = {eng},
number = {1},
pages = {347-356},
title = {Decomposability of extremal positive unital maps on M₂(ℂ)},
url = {http://eudml.org/doc/281593},
volume = {73},
year = {2006},
}

TY - JOUR
AU - Władysław A. Majewski
AU - Marcin Marciniak
TI - Decomposability of extremal positive unital maps on M₂(ℂ)
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 347
EP - 356
AB - A map φ: Mₘ(ℂ) → Mₙ(ℂ) is decomposable if it is of the form φ = φ₁ + φ₂ where φ₁ is a CP map while φ₂ is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map φ: M₂(ℂ) → M₂(ℂ) we construct concrete maps (not necessarily unital) φ₁ and φ₂ which give a decomposition of φ. We also show that in most cases this decomposition is unique.
LA - eng
KW - positive maps; decomposable maps; face structure
UR - http://eudml.org/doc/281593
ER -