Decomposability of Extremal Positive Maps on M 2 (c)

Abstract

A map ϕ : Mm(C) → Mn(C) is decomposable if it is of the form ϕ = ϕ 1 + ϕ 2 where ϕ 1 is a CP map while ϕ 2 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 : M 2 (C) → M 2 (C) we construct concrete maps ϕ 1 and ϕ 2 which give a decomposition of ϕ. We also show that in most cases… (More)

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