Quantum Entanglement and Quantum Discord of Two-Mode Gaussian States in a Thermal Environment

TL;DR

This paper investigates how quantum entanglement and discord evolve over time for two-mode Gaussian states in a thermal environment, revealing conditions for entanglement sudden death and the asymptotic decay of quantum discord.

Contribution

It provides a detailed analysis of the dynamics of entanglement and quantum discord in Gaussian states within thermal baths, highlighting the effects of temperature on quantum correlations.

Findings

Entanglement remains for all times only at zero temperature.

Entanglement experiences sudden death at non-zero temperatures.

Quantum discord decays gradually and asymptotically over time.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath. This is contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.