# Degree of Quantumness in Quantum Synchronization

## TL;DR

This paper introduces a new measure called the degree of quantumness in quantum synchronization, based on the number of non-commuting observables that synchronize, applicable to various quantum systems and compatible with existing measures.

## Contribution

It proposes a novel quantumness measure for synchronization, linking quantum information techniques with physical synchronization properties, and demonstrates its application in different quantum systems.

## Key findings

- The measure captures different physical properties of quantum synchronization.
- Application to cavity-qubit systems illustrates the measure's effectiveness.
- Discussion of quantumness in quantum van der Pol oscillators expands its scope.

## Abstract

We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.