Generalizing Choi map in $M_3$ beyond circulant scenario

TL;DR

This paper generalizes the Choi map in 3x3 matrices beyond circulant cases, providing conditions for when these maps are decomposable, advancing understanding of positive linear maps in quantum information theory.

Contribution

It introduces a broader class of positive maps in $M_3$, extending Choi's original construction and characterizing their decomposability conditions.

Findings

Provides necessary and sufficient conditions for decomposability.

Extends the family of positive maps beyond circulant scenarios.

Enhances understanding of non-decomposable maps in quantum information.

Abstract

We present a generalization of the family of linear positive maps in $M_3$ proposed thirty years ago by Cho et al. (Linear Algebra Appl. ${\bf 171}$, 213 (1992)) as a generalization of the seminal Choi non-decomposable map. The necessary and sufficient conditions for decomposability are provided.