Complexity of Quantum Trajectories

TL;DR

This paper introduces a data-driven method to measure the complexity of quantum trajectories in open quantum systems, revealing how conservation laws and constraints influence chaos and integrability.

Contribution

It applies intrinsic dimension analysis to quantum trajectories, uncovering signatures of chaos, integrability, and Hilbert-space fragmentation in dissipative quantum systems.

Findings

Intrinsic dimension varies with system dynamics and constraints.

Chaotic Lindblad evolution shows higher intrinsic dimension.

Constraints like integrability reduce the intrinsic dimension.

Abstract

Open quantum systems can be described by unraveling Lindblad master equations into ensembles of quantum trajectories. Here we investigate how the complexity of such trajectories is affected by conservation laws and other dynamical constraints of the underlying Lindblad evolution. We characterize this complexity using a data-driven approach based on the intrinsic dimension, defined as the minimal number of variables required to encode the information contained in a data set. Applying this framework to several systems, including dissipative variants of the quantum top and of the XXZ chain, we find that the intrinsic dimension is sensitive to the structure of their dynamics. The Lindblad evolution in these systems is typically chaotic; in particular, we report new signatures of autonomous chaos in the quantum top. At specific parameter values, however, additional constraints arise: the dynamics becomes integrable, exhibits Hilbert-space fragmentation, or develops a closed BBGKY hierarchy, leading to pronounced minima in the intrinsic dimension. Our approach results in an unsupervised probe of the complexity of dissipative quantum systems that is sensitive to chaos and ergodicity breaking phenomena beyond the initial transient regime.