Mapping cones of positive maps

TL;DR

This paper studies cones of positive maps on B(H), revealing duality properties of symmetric mapping cones and applying these findings to characterize certain positive functionals and states in quantum information theory.

Contribution

It introduces the duality of symmetric mapping cones and applies this to characterize positive functionals and quantum states with strong positivity conditions.

Findings

Dual cone of a symmetric mapping cone is also symmetric.

Characterizations of positive functionals with strong positivity conditions.

Applications to separable and PPT-states in quantum information.

Abstract

This is a revised form of the previous paper in which we study cones of positive maps of B(H) into itself. We add the result that the dual cone of a symmetric mapping cone is itself a symmetric mapping cone. As applications we obtain characterizations of linear functionals with strong positivity conditions with respect to a class of mapping cones called symmetric mapping cones. Applications are given to separable and PPT-states.