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.
- Received 25 March 2020
- Accepted 5 April 2021
DOI:https://doi.org/10.1103/PhysRevA.103.042220
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