Entanglement dynamics and quasi-periodicity in discrete quantum walks

TL;DR

This paper investigates how entanglement evolves in discrete quantum walks on finite graphs, revealing various dynamic behaviors including monotonic, oscillatory, and quasi-periodic patterns, with implications for quantum entanglement generation and experimental realization.

Contribution

It characterizes the diverse entanglement dynamics in quantum walks and links these behaviors to system parameters, highlighting potential for experimental observation using optical networks.

Findings

Dynamics can be monotonic, oscillatory, or quasi-periodic.

System sensitivity to parameters resembles chaotic features.

Quantum walk systems can be mapped to optical beamsplitter networks.

Abstract

We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic. While the dynamics of the system are not chaotic since the system comprises linear evolution, the dynamics often exhibit some features similar to chaos such as high sensitivity to the system's parameters, irregularity and infinite periodicity. Our observations are of interest for entanglement generation, which is one primary use for the quantum walk formalism. Furthermore, we show that the systems we model can easily be mapped to optical beamsplitter networks, rendering experimental observation of quasi-periodic dynamics within reach.