Mutual information as an order parameter for quantum synchronization

Abstract

Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently this effect has been analyzed and observed in a number of physical systems close to the quantum mechanical regime. In this work we propose the mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semi-classical to intrinsically quantum mechanical systems. Specifically we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases, independently of the specific details of the system.

Synchronization of micromasers

“…Recent work on coupled quantum van der Pol oscillators has suggested that there may be an intimate connection between the emergence of synchronization in coupled quantum oscillators and the behavior of the mutual information [8,15,19] and it has even been suggested that mutual information could serve as an order parameter for synchronization [15].…”

“…Studies of synchronization effects in the quantum regime have largely concentrated on the behavior of simple model systems such as van der Pol oscillators [7,9,10,12,15,17,19,21] (together with closely related models [22]), though a number of other systems including atomic ensembles [13,16] and optomechanical oscillators [5,6,12,18] have also been investigated. In this article we investigate synchronization in a very different model system consisting of two weakly coupled micromasers.…”

“…In the last few years there has been considerable interest in studying the synchronization of oscillators and related systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] close to threshold or at low excitation levels where semiclassical approaches break down and fully quantum mechanical calculations are required. Recent theoretical work has explored different ways of quantifying synchronization in quantum oscillators [5,7,14,15,20], as well as investigating the connection between it and measures of correlation such as mutual information and entanglement [5,8,10,15,19]. Detailed comparisons have also been made between the predictions of quantum models and those of related semiclassical or classical descriptions [7,12].…”

Synchronizing quantum harmonic oscillators through two-level systems

“…Mutual information and specific correlations have been used, not only as a signature of dynamical alignment of quantum systems, but also to evaluate the degree of synchronization [14][15][16].…”

Influence of relativistic effects on satellite-based clock synchronization

“…Recently, quantum strategies have been exploited to improve the accuracy of clock synchronization. A few quantum clock synchronization (QCS) proposals [5][6][7][8][9][10][11][12][13][14][15][16] and experiments [17] are reported. It is shown that the schemes based on quantum mechanics can gain significant improvements in precision over their classical counterparts.…”