English

Local Probability Conservation in Discrete Time Quantum Walks

Quantum Physics 2021-05-05 v1

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.

Keywords

Cite

@article{arxiv.1909.08569,
  title  = {Local Probability Conservation in Discrete Time Quantum Walks},
  author = {Samuel T. Mister and Benjamin J. Arayathel and Anthony J. Short},
  journal= {arXiv preprint arXiv:1909.08569},
  year   = {2021}
}

Comments

6 pages, 3 figures

R2 v1 2026-06-23T11:19:26.226Z