Entanglement dynamics via coherent-state propagators

TL;DR

This paper develops a semiclassical approach to analyze entanglement dynamics in bipartite systems, linking quantum entanglement measures to classical trajectory stability, and validates it with coupled harmonic oscillators.

Contribution

It introduces a novel semiclassical formula for entanglement evolution based on coherent-state propagators, connecting quantum and classical dynamics.

Findings

The semiclassical formula accurately predicts short-time entanglement.

Application to coupled oscillators shows strong agreement with quantum results.

Provides a unified approach combining propagator and its conjugate.

Abstract

The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a generic Hamiltonian, and derive a formula for the linear entropy of the reduced density matrix using the semiclassical propagator in the coherent-state representation. The formula is explicitly written in terms of quantities that define the stability of classical trajectories of the underlying classical system. The formalism is then applied to the problem of two nonlinearly coupled harmonic oscillators and the result is shown to be in remarkable agreement with the exact quantum measure of entanglement in the short-time regime. An important byproduct of our approach is a unified semiclassical formula which contemplates both the coherent-state propagator and its complex conjugate.