Superposed quantum evolutions across chaotic and regular regimes

TL;DR

This paper investigates how superposing quantum evolutions with regular and chaotic classical limits affects entropy production, revealing complex interactions between classical chaos and quantum interference.

Contribution

It demonstrates that superposing regular and chaotic quantum evolutions can lead to higher entropy than classical mixtures, influenced by classical phase space structure.

Findings

Superposition of regular and chaotic evolutions can exceed classical mixture entropy.

Entropy production depends on the classical phase space structure.

Increased entropy can occur even in regular dynamics with proper post-selection.

Abstract

While the superposition of quantum evolutions is known to produce interference effects, the interference between evolutions with regular and chaotic classical limits remains largely unexplored. Here, we use a Mach-Zehnder interferometer to investigate the superposition of two quantum evolutions, implemented via post-selection, and to compare it with the corresponding classical mixture. The quantum kicked top provides a natural platform for this study, as its classical dynamics ranges from regular to mixed to fully chaotic depending on the Hamiltonian parameters. We show that when a regular evolution is superposed with a chaotic one, the resulting subsystem entropy can exceed that of the classical mixture, provided the contribution of the chaotic branch dominates in the superposed quantum evolution. We further demonstrate that entropy production in such superpositions is strongly influenced by the structure of the underlying classical phase space. We further show that increased entropy generation can occur for purely regular dynamics at small values of the chaos parameter, given an appropriate choice of post-selection. These results reveal a nontrivial interplay between classical chaos and quantum interference in superposed quantum dynamics