Geometric interpretation of the geometric discord

TL;DR

This paper explores the geometric measure of quantum discord, providing visual insights into its behavior for Bell-diagonal states, revealing nonanalyticities under decoherence, and examining hierarchical relationships with original discord.

Contribution

It offers a geometric interpretation of quantum discord, analyzes its behavior under decoherence, and investigates the relationship between geometric and original discord measures.

Findings

Geometric discord exhibits nonanalytic behavior under decoherence.

Constant geometric discord under phase-flip requires initial states to be separable.

Hierarchical relationships between geometric and original discord are verified.

Abstract

We investigate the level surfaces of geometric measure of quantum discord, and provide a pictorial interpretation of geometric discord for Bell-diagonal states. We have observed its nonanalytic behavior under decoherence employing this approach and interestingly found if we expect geometric discord to remain constant under phase-flip channel for a finite period, the initial state must be separable. Besides, this geometric understanding can be applied to verify the hierarchical relationships between geometric discord and the original one. The present work makes us conjecture that the incompatibility of these two definitions may originate from the discrepancy of the geometric structures of them.