Untangling entanglement and chaos

TL;DR

This paper introduces a method to estimate the maximum entanglement in spin systems using the Fannes-Audenaert inequality, revealing how entanglement relates to chaos and state proximity to spin coherent states.

Contribution

The authors develop a novel upper bound estimation technique for entanglement in spin systems, linking entanglement growth to state distance from spin coherent states and validating it with a quantum kicked top model.

Findings

Upper bound effectively estimates entanglement in regular and chaotic regimes.

Entanglement bounds are higher in chaotic regions in the semiclassical limit.

In deep quantum regimes, entanglement bounds are high regardless of chaos.

Abstract

We present a method to calculate an upper bound on the generation of entanglement in any spin system using the Fannes-Audenaert inequality for the von Neumann entropy. Our method not only is useful for efficiently estimating entanglement, but also shows that entanglement generation depends on the distance of the quantum states of the system from corresponding minimum-uncertainty spin coherent states (SCSs). We illustrate our method using a quantum kicked top model, and show that our upper bound is a very good estimator for entanglement generated in both regular and chaotic regions. In a deep quantum regime, the upper bound on entanglement can be high in both regular and chaotic regions, while in the semiclassical regime, the bound is higher in chaotic regions where the quantum states diverge from the corresponding SCSs. Our analysis thus explains previous studies and clarifies the relationship between chaos and entanglement.