arXiv:2607.19328

Quantum Synchronization

Parvinder Solanki, Albert Cabot, Fernando Iemini, Federico Carollo, Midhun Krishna, Yeshma Ibrahim, Michal Hajdušek, Igor Lesanovsky, Rosario Fazio, Roberta Zambrini, Sai Vinjanampathy

quant-phcond-mat.quant-gascond-mat.stat-mechphysics.atom-phphysics.opticsSubmitted Jul 21, 2026• Announced Jul 22, 2026• 0 citations

arXiv HTML PDF

Abstract

Natural and engineered classical systems are replete with examples of synchronization, understood as the adjustment of rhythms of physical systems. Such synchronization is at the heart of the stability of several classical technologies, such as mechanical bridges and electrical networks. Given the advent of quantum simulation and computation technologies, it is natural to study a quantum analogue of synchronization and explore novel applications. This review surveys synchronization in few and many-body quantum systems, measures that quantify them, and their applications to quantum technologies.

Comments: 49 pages, 13 figures, comments welcome

Related papers

Synchronization, quantum correlations and entanglement in oscillator networks

Gonzalo Manzano, Fernando Galve, Gian Luca Giorgi +2 more

Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.

arXiv:1302.3810Scientific ReportsMar 14, 2013167 citations

Synchronization in the quantum regime

Finn Schmolke, Eric Lutz

Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.

quant-pharXiv:2606.21226Jun 22, 20260 citations

Quantum synchronization: A tutorial guide

Sourabh Lahiri, Shamik Gupta

Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.

quant-pharXiv:2609.14375Sep 15, 20260 citations

Generalized measure of quantum synchronization

Noufal Jaseem, Michal Hajdušek, Parvinder Solanki +3 more

We present a generalized information-theoretic measure of synchronization in quantum systems.This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks.Furthermore, the new measure allows us to discuss synchronization of disparate physical systems such as coupled hybrid quantum systems and coupled systems undergoing mutual synchronization that are also driven locally.In many cases of interest, we find a closed-form expression for the proposed measure.

arXiv:2006.13623Physical Review ResearchNov 30, 202058 citations

Properties and relative measure for quantifying quantum synchronization

Wenlin Li, Wen-Zhao Zhang, Chong Li +1 more

Although quantum synchronization phenomena and corresponding measures have been widely discussed recently, it is still an open question how to characterize directly the influence of nonlocal correlation, which is the key distinction for identifying classical and quantum synchronizations. In this paper, we present basic postulates for quantifying quantum synchronization based on the related theory in Mari's work [Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605], and we give a general formula of a quantum synchronization measure with clear physical interpretations. By introducing Pearson's parameter, we show that the obvious characteristics of our measure are the relativity and monotonicity. As an example, the measure is applied to describe synchronization among quantum optomechanical systems under a Markovian bath. We also show the potential by quantifying generalized synchronization and discrete variable synchronization with this measure.

Physical review. EJul 14, 201749 citations

Quantum manifestations of converse symmetry breaking

Daniel P. Buser, Biswabibek Bandyopadhyay, Adilson E. Motter

Quantum synchronization holds promise in advancing quantum technologies such as sensing, communication, and computation. A key challenge in this rapidly developing field is to identify mechanisms that can promote the emergence of synchronous dynamics. Here, we show that quantum synchronization can be enhanced by introducing controlled heterogeneity in the form of coupling mismatches. Using spin van der Pol oscillators as a model system, we show that this mechanism constitutes a quantum analog of the phenomenon of converse symmetry breaking previously identified in classical oscillator networks, where a synchronous state is stabilized by explicit symmetry breaking. We quantify how quantum effects modify this behavior by tuning the degree of quantumness through variations of the spin quantum number. These findings suggest that quantum synchronization can be enhanced in experiments by harnessing rather than suppressing heterogeneity.

quant-pharXiv:2610.40762Nov 2, 2026