Quantum random walks with decoherent coins

Todd A. Brun, H. A. Carteret, and Andris Ambainis
Phys. Rev. A 67, 032304 – Published 14 March 2003
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Abstract

The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum “coin” which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and show that in the long-time limit the variance grows linearly with time, unlike the unitary walk. We compare this to the results of direct numerical simulation, and see how the form of the position distribution changes from the unitary to the usual classical result as we increase the strength of the decoherence.

  • Received 29 October 2002

DOI:https://doi.org/10.1103/PhysRevA.67.032304

©2003 American Physical Society

Authors & Affiliations

Todd A. Brun1,*, H. A. Carteret2,†, and Andris Ambainis1,‡

  • 1Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
  • 2Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

  • *Electronic address: tbrun@ias.edu
  • Electronic address: hcartere@cacr.math.uwaterloo.ca
  • Electronic address: ambainis@ias.edu

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Vol. 67, Iss. 3 — March 2003

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