Quantum versus classical correlations in Gaussian states

TL;DR

This paper analytically calculates quantum discord and classical correlations in all two-mode Gaussian states, revealing that most possess quantum correlations and establishing bounds related to entanglement.

Contribution

It provides the first analytical expressions for quantum discord in all two-mode Gaussian states and explores the relationship between entanglement and classical correlations.

Findings

Almost all two-mode Gaussian states have quantum correlations.

Separable states have discord smaller than unity.

Derived bounds on discord for given entanglement.

Abstract

Quantum discord, a measure of genuinely quantum correlations, is generalized to continuous variable systems. For all two-mode Gaussian states, we calculate analytically the quantum discord and a related measure of classical correlations, solving an optimization over all Gaussian measurements. Almost all two-mode Gaussian states are shown to have quantum correlations, while for separable states, the discord is smaller than unity. For a given amount of entanglement, it admits tight upper and lower bounds. Via a duality between entanglement and classical correlations, we derive a closed formula for the Gaussian entanglement of formation of all mixed three-mode Gaussian states whose normal mode decomposition includes two vacua.