Bell diagonal states with maximal abelian symmetry

TL;DR

This paper introduces a class of 2-qudit states with maximal abelian symmetry, providing necessary and sufficient conditions for their separability, which can serve as benchmarks in entanglement theory research.

Contribution

It generalizes a known construction for d=3 to broader cases and offers a simple framework for analyzing separability in symmetric 2-qudit states.

Findings

Derived necessary and sufficient separability conditions

Generalized Horodecki's construction for d=3

Proposed states as tools for entanglement testing

Abstract

We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a byproduct we generalize well known construction provided by Horodecki et al. for d=3. It is hoped that these states with known separability/entanglement properties may be used to test various notions in entanglement theory.