Local probability conservation in discrete-time quantum walks

Samuel T. Mister, Benjamin J. Arayathel, and Anthony J. Short
Phys. Rev. A 103, 042220 – Published 27 April 2021

Abstract

We show that probability is locally conserved in discrete-time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any unitary evolution of a particle which respects that locality structure, we can define probability currents which also respect the locality structure and which yield the correct final probability distribution.

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  • Received 25 March 2020
  • Accepted 5 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.042220

©2021 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Samuel T. Mister*, Benjamin J. Arayathel, and Anthony J. Short

  • H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom

  • *samuel.mister@bristol.ac.uk
  • ben.arayathel@gmail.com
  • tony.short@bristol.ac.uk

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Issue

Vol. 103, Iss. 4 — April 2021

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