Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems

TL;DR

This paper explores how classical dynamical systems can exhibit a form of entanglement, called epistemic entanglement, arising from non-generating phase space partitions, challenging the classical notion of separability.

Contribution

It introduces the concept of epistemic entanglement in classical systems and demonstrates its emergence through non-generating phase space partitions, with explicit examples involving coupled oscillators.

Findings

Epistemic entanglement occurs in classical systems with non-generating partitions.

Explicit states of coupled oscillators exhibit epistemic entanglement.

Classical states can show entanglement-like properties under certain epistemic conditions.

Abstract

Quantum entanglement relies on the fact that pure quantum states are dispersive and often inseparable. Since pure classical states are dispersion-free they are always separable and cannot be entangled. However, entanglement is possible for epistemic, dispersive classical states. We show how such epistemic entanglement arises for epistemic states of classical dynamical systems based on phase space partitions that are not generating. We compute epistemically entangled states for two coupled harmonic oscillators.