Indecomposable positive maps in low dimensional matrix algebras
Consider a linear map from the n by n matrix algebra \(M_ n({\mathbb{C}})\) into itself. The map is said to be positive if it sends the subset of positive semidefinite matrices into itself. This paper continues the work of \textit{M. D. Choi} [Proc. Symp. Pure Math. 38, Part 2, Kingston/Ont. 1980, 583-590 (1982; Zbl 0522.46037)] and of \textit{K. Tanahashi} and \textit{J. Tomiyama} [Can. Math. Bull. 31, No.3, 308- 317 (1988; Zbl 0679.46044)] on the question of decomposing positive linear maps into a sum of completely positive and completely copositive components. In particular, the author analyzes the degree of indecomposability of certain positive linear maps on \(M_ n({\mathbb{C}})\) for \(n=4,5\).
scientific article; zbMATH DE number 4212237