Entanglement generation and evolution in open quantum systems

TL;DR

This paper investigates how entanglement in a two-oscillator quantum system evolves over time when interacting with an environment, revealing conditions for entanglement preservation, sudden death, or revival.

Contribution

It provides an exact solution to the master equation for Gaussian states and analyzes entanglement dynamics using the Peres-Simon criterion and logarithmic negativity.

Findings

Entanglement can be preserved or destroyed depending on environmental parameters.

Entanglement sudden death and revival phenomena are demonstrated.

The degree of entanglement is quantified by logarithmic negativity over time.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain 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, entanglement sudden death or a periodic collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.