Recurrences in three-state quantum walks on a plane

B. Kollár, M. Štefaňák, T. Kiss, and I. Jex
Phys. Rev. A 82, 012303 – Published 6 July 2010

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.

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  • Received 2 May 2010

DOI:https://doi.org/10.1103/PhysRevA.82.012303

©2010 American Physical Society

Authors & Affiliations

B. Kollár1, M. Štefaňák2,*, T. Kiss1,†, and I. Jex2

  • 1Department of Quantum Optics and Quantum Information, Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary
  • 2Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1—Staré Město, Czech Republic

  • *Correspondence to: martin.stefanak@fjfi.cvut.cz
  • tkiss-libri@szfki.hu

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Vol. 82, Iss. 1 — July 2010

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