Quantum walks with random phase shifts

Jozef Košík, Vladimír Bužek, and Mark Hillery
Phys. Rev. A 74, 022310 – Published 9 August 2006

Abstract

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts “simplify” the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.

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  • Received 29 August 2005

DOI:https://doi.org/10.1103/PhysRevA.74.022310

©2006 American Physical Society

Authors & Affiliations

Jozef Košík1,2, Vladimír Bužek1,3, and Mark Hillery4

  • 1Research Center for Quantum Information, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia
  • 2Quniverse, Líščie údolie 116, 841 04 Bratislava, Slovakia
  • 3Abteilung für Quantenphysik, Universität Ulm, 89069 Ulm, Germany
  • 4Department of Physics, Hunter College of CUNY, 695 Park Avenue, New York, New York 10021, USA

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Issue

Vol. 74, Iss. 2 — August 2006

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