Asymptotic entanglement in 1D quantum walks with a time-dependent coined

TL;DR

This paper analyzes the long-term behavior of entanglement between coin and position in a 1D quantum walk with a time-dependent coin, providing analytical conditions for maximal entanglement.

Contribution

It offers an analytical study of asymptotic coin-position entanglement in inhomogeneous quantum walks with variable coin parameters.

Findings

Identifies conditions for maximal entanglement.

Provides analytical expressions for entanglement behavior.

Explores parameter space for entanglement dynamics.

Abstract

Discrete-time quantum walk evolve by a unitary operator which involves two operators a conditional shift in position space and a coin operator. This operator entangles the coin and position degrees of freedom of the walker. In this paper, we investigate the asymptotic behavior of the coin position entanglement (CPE) for an inhomogeneous quantum walk which determined by two orthogonal matrices in one-dimensional lattice. Free parameters of coin operator together provide many conditions under which a measurement perform on the coin state yield the value of entanglement on the resulting position quantum state. We study the problem analytically for all values that two free parameters of coin operator can take and the conditions under which entanglement becomes maximal are sought.