Decomposable of positive map from M3(C) to M2(M2(C))

Abstract

In most literature, the decomposition of positive maps from M3 to M2 are discussed where the matrix elements are complex numbers. In this paper we construct a positive maps φ(µ,c1,c2) from M3(C) to M2(M2(C)). The Choi matrices for complete positivity and complete copositivity ares visualized as tensor matrix M3 ⊗M2 with M2(C) as the entry elements. The construction allow us describe decomposability on positive semidefinite matrices.