Asymptotic distributions of quantum walks on the line with two entangled coins

Asymptotic distributions of quantum walks on the line with two entangled coins We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero limiting probabilities (localization), thereby distinguishing them from the quantum walks on the line in the basic scenario (i.e., driven by a single coin). In this work, asymptotic position distributions of the quantum walks are examined. We derive a weak limit for the quantum walks and explicit formulas for the limiting probability distribution, whose dependencies on the coin parameter and the initial state of quantum walks are presented. In particular, it is shown that the weak limit for the present quantum walks can be of the form in the basic scenario of quantum walks on the line, for certain initial states of the walk and certain values of the coin parameter. In the case where localization occurs, we show that the limiting probability decays exponentially in the absolute value of a walker’s position, independent of the parity of time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Asymptotic distributions of quantum walks on the line with two entangled coins

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Publisher
Springer US
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Physics; Data Structures, Cryptology and Information Theory; Quantum Physics; Quantum Information Technology, Spintronics; Mathematical Physics; Quantum Computing
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-012-0361-3
Publisher site
See Article on Publisher Site

References

  • An example of a difference between quantum and classical random walks
    Childs, A.; Farhi, E.; Gutmann, S.
  • Quantum random walks in one dimension
    Konno, N.
  • Asymptotic evolution of quantum walks with random coin
    Ahlbrecht, A.; Vogts, H.; Werner, A.H.; Werner, R.F.

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