The connection between phase synchronization in simple nonlinear system and stationary state entanglement in its quantum counterpart

TL;DR

This paper explores the link between phase synchronization in classical nonlinear systems and stationary entanglement in their quantum counterparts, revealing that synchronized states correspond to entangled stationary quantum states.

Contribution

It introduces a quantum model corresponding to a classical nonlinear system and demonstrates that stationary states are both pure and entangled, highlighting a potential general connection.

Findings

Stationary states are pure and entangled.

Small phase dispersion correlates with entanglement.

The classical-quantum connection may be widespread.

Abstract

We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the appropriate Lindblad master equation for the density matrix of two qubit realization of such system we have revealed that stationary state of this composite system is pure and entangled with small dispersion of phase observable. We believe that such curious connection between entangled stationary states of quantum composite system and phase sychronization between its subsystems may be typical for rather wide class of similar nonlinear open systems as well.