Degree of Quantumness in Quantum Synchronization

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.The authors thank L. Garcia-Alvarez, I. L. Egusquiza, R. Zambrini and F. Deppe for fruitful discussions. D.Z.R. acknowledges support from Sao Paulo Research Foundation (FAPESP) Grants No. 2013/23512-7 and No. 2014/24576-1. While M.S. and E.S. are grateful for the funding from Spanish MCIU/AEI/FEDER (PGC2018-095113-B-I00), Basque Government Grant No. IT986-16, the projects QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies and the EU FET Open Grant Quromorphic (828826). This work is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) quantum algorithm teams program, under field work proposal number ERKJ333