Quantum correlations as probes of chaos and ergodicity

TL;DR

This paper investigates how long-time average quantum correlations in a multi-qubit kicked top reflect classical phase space structures, providing numerical and experimental evidence of quantum signatures of chaos across different regimes.

Contribution

It demonstrates the correspondence between quantum correlation measures and classical chaos structures in both semiclassical and deep quantum regimes, including experimental validation.

Findings

Quantum correlations reproduce classical phase space structures.

Experimental data supports quantum-classical correspondence.

Different quantum correlation measures show both similarities and differences.

Abstract

Long-time average behavior of quantum correlations in a multi-qubit system, collectively modeled as a kicked top, is addressed here. The behavior of dynamical generation of quantum correlations such as entanglement, discord, concurrence, as previously studied, and Bell correlation function and tangle, as identified in this study, is a function of initially localized coherent states. Their long-time average reproduces coarse-grained classical phase space structures of the kicked top which contrast, often starkly, chaotic and regular regions. Apart from providing numerical evidence of such correspondence in the semiclassical regime of a large number of qubits, we use data from a recent transmons based experiment to explore this in the deep quantum regime of a 3-qubit kicked top. The degree to which quantum correlations can be regarded as a quantum signature of chaos, and in what ways the various correlation measures are similar or distinct are discussed.