Recurrences in three-state quantum walks on a plane

B. Kollár, M. Štefaňák, T. Kiss, I. Jex

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Abstract

We analyze the role of dimensionality in the time evolution of discrete-time quantum walks through the example of the three-state walk on a two-dimensional triangular lattice. We show that the three-state Grover walk does not lead to trapping (localization) or recurrence to the origin, in sharp contrast to the Grover walk on the two-dimensional square lattice. We determine the power-law scaling of the probability at the origin with the method of stationary phase. We prove that only a special subclass of coin operators can lead to recurrence, and there are no coins that lead to localization. The propagation for the recurrent subclass of coins is quasi-one dimensional.

Original languageEnglish
Article number012303
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume82
Issue number1
DOIs
Publication statusPublished - Jul 6 2010

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ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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