Journal of Statistical Physics

, Volume 147, Issue 4, pp 832–852 | Cite as

Open Quantum Random Walks

Article

Abstract

A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains. We explore the “quantum trajectory” point of view on these quantum random walks, that is, we show that measuring the position of the particle after each time-step gives rise to a classical Markov chain, on the lattice times the state space of the particle. This quantum trajectory is a simulation of the master equation of the quantum random walk. The physical pertinence of such quantum random walks and the way they can be concretely realized is discussed. Differences and connections with the already well-known quantum random walks, such as the Hadamard random walk, are established.

Keywords

Quantum random walks Open quantum systems Quantum mechanics Markov chains 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • S. Attal
    • 1
  • F. Petruccione
    • 2
  • C. Sabot
    • 1
  • I. Sinayskiy
    • 2
  1. 1.Institut Camille JordanUniversité de Lyon, Université de Lyon 1, C.N.R.S.Villeubanne cedexFrance
  2. 2.Quantum Research Group, School of Physics and National Institute for Theoretical PhysicsUniversity of KwaZulu-NatalDurbanSouth Africa

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