Diagnosing quantum chaos with out-of-time-ordered-correlator quasiprobability in the kicked-top model

TL;DR

This paper introduces a new quasi-probability distribution based on out-of-time-ordered correlators (OTOCs) to diagnose quantum chaos in the kicked-top model, revealing its relation to entanglement and outperforming traditional measures.

Contribution

The study presents a novel quasi-probability distribution derived from OTOCs as a tool to characterize quantum chaos, providing a more effective measure than existing methods.

Findings

Nonclassicality of the distribution correlates with chaotic behavior.

Initial states in the 'sea of chaos' show increased entanglement and chaos signatures.

The OTOC-based measure outperforms traditional chaos indicators.

Abstract

While classical chaos has been successfully characterized with consistent theories and intuitive techniques, such as with the use of Lyapunov exponents, quantum chaos is still poorly understood, as well as its relation with multi-partite entanglement and information scrambling. We consider a benchmark system, the kicked top model, which displays chaotic behaviour in the classical version, and proceed to characterize the quantum case with a thorough diagnosis of the growth of chaos and entanglement in time. As a novel tool for the characterization of quantum chaos, we introduce for this scope the quasi-probability distribution behind the out-of-time-ordered correlator (OTOC). We calculate the cumulative nonclassicality of this distribution, which has already been shown to outperform the simple use of OTOC as a probe to distinguish between integrable and nonintegrable Hamiltonians. To provide a thorough comparative analysis, we contrast the behavior of the nonclassicality with entanglement measures, such as the tripartite mutual information of the Hamiltonian as well as the entanglement entropy. We find that systems whose initial states would lie in the "sea of chaos" in the classical kicked-top model, exhibit, as they evolve in time, characteristics associated with chaotic behavior and entanglement production in closed quantum systems. We corroborate this indication by capturing it with this novel OTOC-based measure.