Accelerated quantum walk, two-particle entanglement generation and localization

TL;DR

This paper explores how accelerating discrete-time quantum walks influence entanglement and localization, revealing new insights into relativistic quantum dynamics and potential quantum simulation applications.

Contribution

It introduces a scheme for accelerated quantum walks, demonstrating enhanced entanglement and localization transition, linking acceleration with quantum entanglement and disorder effects.

Findings

Acceleration enhances entanglement between particle and position space.

Disorder induces transition from localization to delocalization.

Quantum walks can model relativistic quantum phenomena.

Abstract

We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and two-particle in position space. We show the effect of acceleration in enhancing the entanglement between the particle and position space in one-particle quantum walk and in generation of entanglement between the two unentangled particle in two-particle quantum walk. By introducing the disorder in the form of phase operator we study the transition from localization to delocalization as a function of acceleration. These inter-winding connection between acceleration, entanglement generation and localization along with well established connection of quantum walks with Dirac equation can be used to probe further in the direction of understanding the connection between acceleration, mass and entanglement in relativistic quantum mechanics and quantum field theory. Expansion of operational tools for quantum simulations and for modelling quantum dynamics of accelerated particle using quantum walks is an other direction where these results can play an important role.