Entanglement and its relationship to classical dynamics

TL;DR

This paper investigates how quantum entanglement in the quantum kicked top relates to classical phase space, revealing strong correlations with initial conditions and symmetry points, independent of chaos.

Contribution

It demonstrates a novel connection between classical phase space structures and quantum entanglement, introducing a new measure that better predicts entanglement behavior.

Findings

Entanglement correlates with classical phase space features.

Initial condition dependence of entanglement is organized around symmetry points.

Entanglement shows periodicity with respect to kicks and kick strength.

Abstract

We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement $S_Q$ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of $S_Q$ even for the extreme case of two spin-$1/2$ qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.