Witnessed entanglement and the geometric measure of quantum discord

TL;DR

This paper explores the relationship between geometric quantum discord and entanglement measures using witness operators, providing new bounds and relations, especially between negativity and geometric discord, with numerical illustrations.

Contribution

It establishes new relations between geometric quantum discord and entanglement measures, improving bounds by redefining discord with the trace norm.

Findings

Relation between negativity and geometric discord in Hilbert-Schmidt norm

Improved bounds on geometric discord using trace norm

Numerical illustrations supporting theoretical results

Abstract

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.