Classical Entanglement and Entropy

TL;DR

This paper explores the relationship between quantum and classical entanglement entropy, demonstrating that for weakly coupled harmonic oscillators, the quantum entanglement entropy matches the classical counterpart, indicating classical nature of the entanglement.

Contribution

It establishes a direct equivalence between quantum and classical entanglement entropy in a specific harmonic oscillator model, highlighting the classical nature of certain quantum entanglement.

Findings

Quantum and classical entanglement entropies are equal in the studied model.

The reduced density matrix is close to a maximally entangled state.

Entanglement in this context is shown to be purely classical.

Abstract

Motivated by recent discussions of entanglement in the context of high energy scattering, we consider the relation between the entanglement entropy of a highly excited state of a quantum system and the classical entanglement entropy of the corresponding classical system. We show on the example of two weakly coupled harmonic oscillators, that the two entropies are equal. Quantum mechanically, the reduced density matrix which yields this entropy is close to the maximally entangled state. We thus observe that the nature of entanglement in this type of state is purely classical.