Influence of generic quantum coins on the spreading and entanglement in binary aperiodic quantum walks

TL;DR

This study investigates how different quantum coins influence the spreading and entanglement in binary quantum walks with sequences like Fibonacci, Thue-Morse, and Rudin-Shapiro, revealing localized behaviors and parameter tuning effects.

Contribution

It introduces a comprehensive numerical analysis of the impact of generic quantum coins on inhomogeneous quantum walks with various sequences, highlighting the role of coin parameters in controlling dynamics.

Findings

Fibonacci walk can exhibit localized behavior for certain coin parameters.

A specific coin parameter can significantly tune spreading and entanglement.

Increasing the parameter enhances both position spread and hybrid entanglement.

Abstract

Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of generic quantum coins on the hybrid entanglement and spreading behavior of different binary quantum walks with time and position dependent coin operations based on the Fibonacci, Thue-Morse and Rudin-Shapiro sequences. We find that each considered walk is differently but significantly influenced by the choice of quantum coins. We demonstrate that the dynamic Fibonacci walk exhibits localized behavior for certain coin parameters. This behavior brings new information about the role played by dynamic coin disorder, considered before as always a generator of non-localized behavior. We also reveal the significant role played by a specific coin parameter which controls the nature of superposition of spin up and spin down states during coin operation. We find that the parameter can distinctly tune the spreading and entanglement behavior of a binary quantum walk. We show that an increase in the value of the parameter can enhance both the the standard deviation of the position distribution of the walker and the hybrid entanglement from significantly low to significantly high values depending on the coin and the nature of coin operations. The present work may thus be considered as one step towards understanding the role of coins in inhomogeneous quantum walks.