Comment on "Entanglement and chaos in the kicked top"

TL;DR

This paper critically examines the relationship between chaos and entanglement in the kicked top, clarifying previous findings and exploring how initial state localization and system chaoticity influence entanglement dynamics.

Contribution

It provides clarifications on prior results, analyzes the impact of initial state localization near regular-chaotic boundaries, and discusses entanglement as a chaos indicator.

Findings

Entanglement can occur for states near the boundary between regular and chaotic regions.

Increasing system chaoticity enhances the correlation between chaos and entanglement.

Entanglement's role as a chaos signature depends on initial state localization and system parameters.

Abstract

We comment on the investigation of the connection between chaos and dynamically generated entanglement in Phys. Rev. E, \textbf{83}, 016207, (2011). While, in the referred paper, the authors give an explicit example of a state initially localized in the regular region and still has entanglement properties similar to the states localized in the chaotic region, a few clarifications related to previous works are in order. Firstly, it is crucial to point out that such a behavior can occur for states initially localized near the border between the chaotic region and regular island, which seems to be the case in the example provided in the referred paper. We comment on the time evolution of such states and the extent to which these can be regarded as having "regular dynamics". Secondly, the degree to which entanglement is correlated with the chaos in the system is better understood when we analyze the same initial state and increase the chaoticity in the system gradually. We also discuss in what capacity entanglement can be regarded as a signature of chaos in such studies.