Decomposability of extremal positive unital maps on $M_2$

Details Decomposability of extremal positive unital maps on $M_2$ Decomposability of extremal positive unital maps on $M_2$

2005-09-30

arxiv.org/abs/math/0510005v2

Mathematics

Functional Analysis

9 pages

Scientific paper

A map $\phi:M_m(\bC)\to M_n(\bC)$ is decomposable if it is of the form $\phi=\phi_1+\phi_2$ where $\phi_1$ is a CP map while $\phi_2$ 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 $\phi:M_2(\bC)\to M_2(\bC)$ we construct concrete maps (not necessarily unital) $\phi_1$ and $\phi_2$ which give a decomposition of $\phi$. We also show that in most cases this decomposition is unique.

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