Measurement-induced disturbances and nonclassical correlations of Gaussian states

TL;DR

This paper investigates quantum correlations in two-mode Gaussian states using measurement-induced disturbance (MID) and its optimized version (AMID), revealing the importance of non-Gaussian measurements for accurately quantifying and exploiting these correlations.

Contribution

It introduces a Gaussian AMID constrained to Gaussian measurements, explicitly solves the optimization for key state families, and highlights the role of non-Gaussian measurements in quantum correlation assessment.

Findings

Gaussian AMID can be optimized with non-Gaussian measurements for certain states.

MID overestimates quantum correlations compared to Gaussian discord.

Bounds for Gaussian AMID are established at fixed Gaussian discord.

Abstract

We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous variable systems, by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states, comprising pure states, where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two--mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states.