We provide the continuation of an analysis of a class of positive maps proposed ten years ago by Kossakowski. In particular, we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory and a certain class of positive maps.
A Class of Extremal Positive Maps in 3×3 Matrix Algebras
We present a general characterization of k-positivity for a positive map in terms of the estimation of the Ky Fan norm of the matrix constructed from the Kraus operators of the associated completely positive map. Combining this with the result given by Takasaki and Tomiyama we construct a family of positive maps between matrix algebras of different dimensions depending on a parameter. The estimate bounds on the parameter to obtain the k-positivity are better than those derived from the spectral conditions considered by Chruściński and Kossakowski. We further look with special attention at the case where we give the precise bound for the regions of decomposability.