Dynamics of Gaussian discord between two oscillators interacting with a common environment

TL;DR

This paper investigates how Gaussian discord evolves between two harmonic oscillators coupled to a common environment, characterizing its asymptotic behavior, optimal measurement strategies, and relation to entanglement dynamics.

Contribution

It provides a detailed analysis of the asymptotic Gaussian discord, including measurement phase diagrams and comparison with true discord, extending previous entanglement studies.

Findings

Gaussian discord reaches a non-zero asymptote depending on environment parameters.

Optimal measurement strategies are characterized by a phase diagram with homodyne and heterodyne phases.

Gaussian discord can overestimate true discord at high temperatures.

Abstract

We analyze the evolution of the Gaussian discord between two resonant harmonic oscillators coupled to a common environment. For this, we use the same tools we applied before to fully characterize the evolution of the entanglement in this system [ Phys. Rev. Lett. 100 220401 (2008)]. The asymptotic value of Gaussian discord is obtained as a function of parameters characterizing the environment (temperature, couplings, etc.) and the initial state of the system (initial squeezing, initial purity, etc.) The type of Gaussian measurement optimizing the extraction of information between the oscillators is fully characterized by means of a phase diagram. Such a diagram (with phases corresponding to homodyne or heterodyne measurements) has similar topology to the one describing dynamical phases for the entanglement. We present evidence pointing to the fact that Gaussian discord is not always a good approximation of true discord as the asymptotic value of the former is shown to be a nondecreasing function of temperature (in the high-temperature regime), reaching an asymptotic value of log(2) for a pure initial state (and lower values for mixed initial states).