A class of optimal positive maps in $M_n$

TL;DR

This paper proves that a specific class of positive maps in matrix algebra $M_n$ are optimal, meaning they cannot be decomposed further into positive maps, generalizing a well-known map in $M_3$.

Contribution

It introduces a new class of optimal positive maps in $M_n$, extending the seminal Choi map in $M_3$ to higher dimensions.

Findings

The class of maps is proven to be optimal.

These maps cannot be decomposed into other positive maps.

The work generalizes the Choi positive map in $M_3$.

Abstract

It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization of a seminal Choi positive map in $M_3$.