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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-27,
author = {W\l adys\l aw A. Majewski and Marcin Marciniak},
title = {Decomposability of extremal positive unital maps on M2(C)},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {347-356},
zbl = {1116.47033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-27}
}
Władysław A. Majewski; Marcin Marciniak. Decomposability of extremal positive unital maps on M₂(ℂ). Banach Center Publications, Tome 72 (2006) pp. 347-356. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-27/