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.
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