Quantum entanglement from classical trajectories

TL;DR

This paper introduces a novel deterministic classical trajectory method to simulate quantum entanglement, accurately capturing coherence and decoherence in mixed quantum-classical systems, offering an alternative to existing stochastic approaches.

Contribution

The authors develop a new approach that models quantum entanglement using independent classical trajectories, derived from a path-integral representation of a spin-1/2 system.

Findings

Accurately reproduces wavepacket splitting in nonadiabatic scattering.

Correctly accounts for coherence and decoherence effects.

Provides an alternative to stochastic surface-hopping methods.

Abstract

A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin-1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wavepacket in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory or semiclassical approaches.