arXiv:1603.03534

All 2-positive linear maps from M3 to M3 are decomposable

Yang Yu, Denny H. Leung, Wai-Shing Tang

Published Mar 11, 2016• 2 citations

arXiv HTML PDF

Abstract

Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k

DOI: 10.48550/arxiv.1603.03534

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arXiv:1603.03534

All 2-positive linear maps from M3 to M3 are decomposable

Yang Yu, Denny H. Leung, Wai-Shing Tang

Published Mar 11, 2016• 2 citations

arXiv HTML PDF

Abstract

Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k

DOI: 10.48550/arxiv.1603.03534

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Generalizing Choi map in

M_3

beyond circulant scenario

We present a generalization of the family of linear positive maps in

M_3

proposed thirty years ago by Cho et al. (Linear Algebra Appl.

{\bf 171}

, 213 (1992)) as a generalization of the seminal Choi non-decomposable map. The necessary and sufficient conditions for decomposability are provided.

On decomposability of positive maps between

M_2

and

M_n

A map $ϕ:M_m(\bC)\to M_n(\bC)$ 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. A partial characterization of decomposability for maps $ϕ: M_2(\bC) \to M_3(\bC)$ is given.

A Class of Extremal Positive Maps in

3 \times 3

Matrix Algebras