Entanglement in open quantum dynamics

TL;DR

This paper investigates how entanglement in a two-oscillator quantum system evolves under environmental influence, revealing conditions for entanglement creation, decay, and steady-state entanglement using Gaussian state analysis.

Contribution

It provides a detailed description of entanglement dynamics in open quantum systems using covariance matrices and the Peres-Simon criterion, including conditions for entanglement sudden death and steady states.

Findings

Entanglement can be generated, lost, or periodically revived depending on environmental parameters.

Certain environments lead to asymptotic entangled states, others to separable states.

The degree of entanglement in steady states is quantified by logarithmic negativity.

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 entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement. We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.