Recurrence and Pólya number of quantum walks

M. Štefaňák, I. Jex, T. Kiss

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78 Citations (Scopus)

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 localization of quantum walks. In contrast with 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 us to change the character of the quantum walk from recurrent to transient by altering the initial state.

Original languageEnglish
Article number020501
JournalPhysical Review Letters
Volume100
Issue number2
DOIs
Publication statusPublished - Jan 14 2008

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Recurrence and Pólya number of quantum walks. / Štefaňák, M.; Jex, I.; Kiss, T.

In: Physical Review Letters, Vol. 100, No. 2, 020501, 14.01.2008.

Research output: Contribution to journalArticle

Štefaňák, M. ; Jex, I. ; Kiss, T. / Recurrence and Pólya number of quantum walks. In: Physical Review Letters. 2008 ; Vol. 100, No. 2.
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