Circulant states with vanishing quantum discord

TL;DR

This paper investigates a class of 2-qudit circulant states, generalizing 2-qubit X-states, and establishes criteria for when these states have zero quantum discord, with a focus on Bell diagonal states.

Contribution

It provides necessary and sufficient conditions for vanishing quantum discord in circulant states, extending the understanding of quantum correlations in higher-dimensional systems.

Findings

Criteria for zero quantum discord in circulant states

Extension of X-states to 2-qudit systems

Analysis of Bell diagonal states as a special case

Abstract

We analyze a class of 2-qudit circulant states. They define generalization of well known 2-qubit X-states. We formula the necessary and sufficient criteria for vanishing quantum discord. We illustrate our analysis by an important subclass of circulant states -- so called Bell diagonal states.