Entanglement dynamics of spins using a few complex trajectories

TL;DR

This paper develops a semiclassical approach using complex trajectories to accurately describe the entanglement dynamics of two spins initially in coherent states, bridging classical and quantum descriptions.

Contribution

It introduces a novel semiclassical formula for entanglement quantification based on a few complex trajectories derived from classical phase space.

Findings

The semiclassical formula matches quantum entanglement dynamics well.

Few complex trajectories are sufficient for accurate results.

The approach applies to a specific physical system with excellent agreement.

Abstract

In this work, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator, assumed as an entanglement quantifier. The resulting expression depends on sets of four trajectories, originated from the underlying classical description, and having mutually connected final phase-space points. Such classical elements, which are capable to reproduce the quantum entanglement even for long values of propagation time, arise when we assume a proper analytical continuation of the classical phase space onto a complex domain. We apply this theory to a particular physical system, showing that taking into account only a few sets of complex trajectories is enough to get an excellent agreement between the semiclassical linear entropy of the reduced density operator and its quantum counterpart.