A class of bistochastic positive optimal maps in $M_d(\mathbb{C})$

TL;DR

This paper generalizes a positive map in complex matrices, proving its optimality and indecomposability, and introduces a new class of PPT entangled states in bipartite quantum systems.

Contribution

It extends a known positive map to higher dimensions and demonstrates its optimality and indecomposability, also producing new PPT entangled states.

Findings

The generalized maps are optimal and indecomposable.

A new class of PPT entangled states is constructed.

The results extend understanding of positive maps in quantum information.

Abstract

We provide a straightforward generalization of a positive map in $M_3(\mathbb{C})$ considered recently by Miller and Olkiewicz \cite{Miller}. It is proved that these maps are optimal and indecomposable. As a byproduct we provide a class of PPT entangled states in $d \otimes d$.