Quantum-classical correspondence in entanglement production: Entropy and classical tori

TL;DR

This paper explores how classical invariant tori influence quantum entanglement production in semiclassical systems, revealing a strong link between classical frequency spectra and quantum entanglement measures.

Contribution

It introduces a frequency entropy measure to connect classical frequency distributions with quantum entanglement, demonstrating a novel semiclassical correspondence.

Findings

Larger classical power spectra correlate with higher entanglement.

Classical frequency entropy aligns with maximum von Neumann entropy.

Entanglement dynamics are governed by classical invariant tori.

Abstract

We analyze the connections between entanglement dynamics and classical trajectories in a semiclassi-cal regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency com-ponents corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution, and find that there is good correspondence between the classical frequency entro-pies and the maximum von Neumann entropies.