Accelerated quantum walk, two-particle entanglement generation and localization

Shivani Singh,Radhakrishnan Balu,C M Chandrashekar,Raymond Laflamme

doi:10.1088/2399-6528/ab1c6e

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.

Highlights

Quantum walks [1,2,3,4] have played an important role in development of various quantum information processing and computation protocols [5,6,7,8]
We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and twoparticle 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

Summary

INTRODUCTION

Quantum walks [1,2,3,4] have played an important role in development of various quantum information processing and computation protocols [5,6,7,8]. We study the two interacting particle discrete-time quantum walk and present the situations where acceleration plays a role in entangling the two initially unentangled particles. These results are in general valid for any time dependent function of coin parameter which introduces acceleration into the dynamics. This shows how the probability amplitude changes from one position to an another for a given time step and the dependence of probability amplitude on the parameter of the evolution operator.

Single-particle

Two-particle

DISORDER AND LOCALIZATION

DISCUSSION AND CONCLUDING