Recurrences in three-state quantum walks on a plane

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

Research output: Contribution to journalArticle

18 Citations (Scopus)


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
Issue number1
Publication statusPublished - Jul 6 2010


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this