Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems

TL;DR

This paper develops a method to analyze the macroscopic behavior of multipartite correlations in permutation-invariant open quantum systems, revealing conditions for extensive mutual information scaling and illustrating with a specific quantum model.

Contribution

It introduces a novel approach to determine the macroscopic steady-state correlations in permutation-invariant quantum systems, extending classical results to quantum regimes.

Findings

Extensive mutual information scaling is not possible for systems relaxing to fixed points.

Robust extensive scaling occurs in systems relaxing to time-dependent attractors like limit cycles.

The method is demonstrated on the driven-dissipative Lipkin-Meshkov-Glick model.

Abstract

Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to determine the macroscopic behavior of the steady-state multipartite mutual information between $N$ interacting units undergoing Markovian evolution that is invariant under unit permutations. Using this approach, we extend a conclusion previously drawn for classical systems that the extensive scaling of mutual information is either not possible for systems relaxing to fixed points of the mean-field dynamics or such scaling is not robust to perturbations of system dynamics. In contrast, robust extensive scaling occurs for system relaxing to time-dependent attractors, e.g., limit cycles. We illustrate the applicability of our method on the driven-dissipative Lipkin-Meshkov-Glick model.