# Decomposability of extremal positive unital maps on M₂(ℂ)

Władysław A. Majewski; Marcin Marciniak

Banach Center Publications (2006)

- Volume: 73, Issue: 1, page 347-356
- ISSN: 0137-6934

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topWładysław 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 -

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