Measures of quantum synchronization in continuous variable systems

TL;DR

This paper introduces two measures for quantifying quantum synchronization in continuous variable systems, extending classical notions and exploring their bounds, connections to entanglement, and applications in opto-mechanics.

Contribution

It presents novel measures for quantum synchronization, analyzes their bounds, and links them to entanglement and practical quantum systems.

Findings

Heisenberg principle bounds complete synchronization.

Phase synchronization measure can be unbounded but limited without quantum resources.

Connections between entanglement and synchronization are elucidated.

Abstract

We introduce and characterize two different measures which quantify the level of synchronization of interacting continuous variable quantum systems. The two measures allow to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is in principle unbounded, however in the absence of quantum resources (e.g. squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum opto-mechanical systems.