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Open Quantum Systems Decoherence
Recurrence and Pólya number of quantum walks
arXiv
Authors: M. Stefanak, I. Jex, T. Kiss
Year
2007
Paper ID
50301
Status
Preprint
Abstract Read
~2 min
Abstract Words
97
Citations
N/A
Abstract
We analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localisation of quantum walks. In contrast to classical walks, where the Pólya number is characteristic for the given dimension, the recurrence probability of a quantum walk depends in general on the topology of the walk, choice of the coin and the initial state. This allows to change the character of the quantum walk from recurrent to transient by altering the initial state.
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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- We analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks.
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