New tools for investigating positive maps in matrix algebras

TL;DR

This paper introduces a new method for constructing positive maps in matrix algebras, enabling the verification of known maps' positivity and the creation of new, indecomposable, and optimal maps with potential applications in quantum entanglement detection.

Contribution

The paper presents a novel tool for constructing and verifying positive maps, including new families of indecomposable and optimal maps, advancing the study of entanglement witnesses.

Findings

Proved positivity of several well-known maps.

Constructed a new family of positive, indecomposable, and optimal maps.

Provided a versatile tool for exploring positive maps in matrix algebras.

Abstract

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as reduction map, generalized reduction, Robertson map, and many others). Furthermore, we use it to construct a new family of linear maps and prove that they are positive, indecomposable and (nd)optimal.