Interplay between computable measures of entanglement and other quantum correlations

TL;DR

This paper explores the relationship between entanglement and quantum correlations in quantum systems, establishing a hierarchy and universal bounds between computable measures like negativity and geometric quantum discord.

Contribution

It demonstrates a fundamental relationship between negativity and geometric quantum discord, extending results to higher-dimensional systems and providing numerical evidence for a universal hierarchy.

Findings

Geometric discord equals squared negativity on pure states.

For mixed states, geometric discord is always greater than or equal to squared negativity.

Numerical evidence supports the hierarchy in higher-dimensional systems.

Abstract

Composite quantum systems can be in generic states characterized not only by entanglement, but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D_G. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship $D_G \geq N^2$ holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, that we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.