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On the structure of positive maps between matrix algebras

100%

Majewski W., Marciniak M.

Banach Center Publications

2007

tom 78

nr 1

249-263

The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.

Decomposability of extremal positive unital maps on M₂(ℂ)

100%

Majewski W., Marciniak M.

Banach Center Publications

2006

tom 73

nr 1

347-356

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.

Ograniczanie wyników

2 Banach Center Publications

2 Majewski W.

2 Marciniak M.

1 2007

1 2006

Wyniki wyszukiwania

On the structure of positive maps between matrix algebras

Decomposability of extremal positive unital maps on M₂(ℂ)