Generalizing Choi-like maps

TL;DR

This paper explores the generalization of Choi-like maps on 3x3 matrices, providing conditions for their positivity and decomposability, which advances understanding of their mathematical properties.

Contribution

It introduces new necessary and sufficient conditions for the positivity and decomposability of generalized Choi maps, extending previous work.

Findings

Identified necessary conditions for positivity of generalized Choi maps.

Established sufficient conditions for positivity and decomposability.

Enhanced understanding of the mathematical structure of generalized Choi maps.

Abstract

A problem of further generalization of generalized Choi maps $\Phi_{[a,b,c]}$ acting on $\mathbb{M}_3$ introduced by Cho, Kye and Lee is discussed. Some necessary conditions for positivity of the generalized maps are provided as well as some sufficient conditions. Also some sufficient condition for decomposability of these maps is shown.