A semiclassically entangled puzzle

TL;DR

This paper explores a semiclassical entanglement puzzle involving two harmonic oscillators, questioning whether nonlinear interactions affect the reduced Wigner function of one subsystem, and discusses speculative ideas about this phenomenon.

Contribution

It introduces a semiclassical perspective on entanglement in harmonic oscillators and raises questions about the effects of nonlinear interactions on reduced states.

Findings

Identifies a potential inconsistency in semiclassical entanglement behavior.

Proposes speculative explanations for the observed puzzle.

Highlights the need for further investigation into semiclassical entanglement dynamics.

Abstract

For a maximally entangled eigenstate of a system of two non-interacting identical one dimensional harmonic oscilators, at the semiclassical level, it is not obviously true that a nonlinear interaction with one of the subsystems leaves the reduced semiclassical Wigner function of the other subsystem unaffected. Once stated, we advance some wild speculations regarding this seeming puzzle.