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arXiv · 1909.08569

Local Probability Conservation in Discrete Time Quantum Walks

Samuel T. Mister·Benjamin J. Arayathel·Anthony J. Short
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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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Samuel T. Mister, Benjamin J. Arayathel, Anthony J. Short. 2019-09-18. Local Probability Conservation in Discrete Time Quantum Walks. https://doi.org/10.1103/physreva.103.042220

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