Tensor products of positive maps of matrix algebras

TL;DR

This paper establishes conditions under which the tensor product of two positive maps between matrix algebras remains positive, focusing on the roles of symmetric mapping cones and their duals.

Contribution

It provides necessary and sufficient conditions for tensor products of positive maps to be positive, linking them to symmetric mapping cones and dual cones.

Findings

Tensor product positivity is characterized by cone membership.

Conditions involve symmetric mapping cones and their duals.

Results generalize previous understanding of positive map tensor products.

Abstract

We give conditions for when the tensor product of two positive maps between matrix algebras is a positive map. This happens when one map belongs to a symmetric mapping cone and the other to the dual cone. Necessary and sufficient conditions are given.