Gaussian geometric discord

TL;DR

This paper extends the geometric measure of quantum discord to continuous variable Gaussian states, providing explicit formulas and bounds for two-mode squeezed thermal states, and discusses alternative geometric correlation measures.

Contribution

It introduces a formalism for Gaussian geometric discord, deriving explicit formulas and bounds for specific states, advancing the quantification of quantum correlations in continuous variable systems.

Findings

Explicit formulas for Gaussian geometric discord in two-mode squeezed thermal states

Bounds for geometric discord under energy constraints

Discussion of alternative geometric correlation measures

Abstract

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states in [B. Dakic, C. Brukner, and V. Vedral, Phys. Rev. Lett. 105, 190502 (2010)], to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.