Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

TL;DR

This paper investigates how classical bifurcations influence quantum correlations in the quantum kicked top, revealing rapid changes near bifurcation points and scaling behaviors linked to chaos and semiclassical limits.

Contribution

It demonstrates the impact of classical bifurcations on quantum correlation measures and provides analytical and numerical insights into their behavior in chaotic and regular regimes.

Findings

Quantum correlations change rapidly near bifurcation points.

In chaotic regimes, correlations align with random matrix theory predictions.

Correlations scale with total spin and exhibit power-law decay near fixed points.

Abstract

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. The measures of quantum correlations do not have a classical analog and yet are influenced by the classical dynamics. In this work, by modelling the quantum kicked top as a multi-qubit system, the effect of classical bifurcations on the measures of quantum correlations such as quantum discord, geometric discord, Meyer and Wallach $Q$ measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of the trivial fixed points of the kicked top, scaling function decays as a power-law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the $Q$ measure. We also suggest that it can have experimental consequences.