Decoherence and asymptotic entanglement in open quantum dynamics

TL;DR

This paper investigates quantum decoherence and entanglement dynamics of harmonic oscillators in open quantum systems, revealing how environmental interactions lead to decoherence and potential asymptotic entanglement.

Contribution

It provides a detailed analysis of decoherence times and demonstrates the emergence of asymptotic entanglement in two oscillators interacting with a common environment.

Findings

Decoherence increases over time, matching the scale of thermal and quantum fluctuations.

Decoherence time is comparable to the time when thermal fluctuations dominate.

Two non-interacting oscillators can become asymptotically entangled in a shared environment.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. Then we solve the master equation for two independent harmonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment become asymptotically entangled for certain environments, so that in the long-time regime they manifest non-local quantum correlations.