Spectral conditions for positive maps

TL;DR

This paper introduces spectral conditions to classify positive linear maps in matrix algebras, generalizing known examples and aiding the study of quantum entanglement.

Contribution

It presents a spectral-based classification of positive maps, extending Choi's example, and constructs maps positive on specific subsets relevant to quantum entanglement.

Findings

Spectral conditions enable classification of positive maps.

Construction of maps positive on convex subsets of separable states.

Generalization of Choi's example of positive but not completely positive maps.

Abstract

We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive. It is shown how the spectral conditions enable one to construct linear maps on tensor products of matrix algebras which are positive but only on a convex subset of separable elements. Such maps provide basic tools to study quantum entanglement in multipartite systems.