Exact analysis of disentanglement for continuous variable systems and application to a two-body system at zero temperature in an arbitrary heat bath

TL;DR

This paper presents an exact method for analyzing decoherence and entanglement in continuous variable quantum systems, applying it to a two-particle Gaussian state in a zero-temperature heat bath, demonstrating entanglement sudden death.

Contribution

It introduces an exact approach based on quantum distribution functions for studying decoherence and entanglement, with explicit results for a two-body system at zero temperature.

Findings

Initial entanglement is confirmed using Duan's criterion.

The system becomes separable after a finite time (entanglement sudden death).

Exact numerical results are provided for a single relaxation time bath at zero temperature.

Abstract

We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to the problem of a pair of particles in a correlated Gaussian state. The initial state and its time development are explicitly exhibited. For a single relaxation time bath at zero temperature exact numerical results are given. The criterion of Duan et al. \cite{duan00} for such states is used to prove that the state is initially entangled and becomes separable after a finite time (entanglement sudden death).