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    • Quantum Random Walks and their Convergence to Evans-Hudson Flows

      Lingaraj Sahu

      Volume 118 Issue 3 August 2008 pp 443-465

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/03/0443-0465

    • Keywords

       

      Quantum dynamical semigroup; Evans–Hudson flow; quantum random walk.

    • Abstract

       

      Using coordinate-free basic operators on toy Fock spaces, quantum random walks are defined following the ideas of Attal and Pautrat. Extending the result for one dimensional noise, strong convergence of quantum random walks associated with bounded structure maps to Evans–Hudson flow is proved under suitable assumptions. Starting from the bounded generator of a given uniformly continuous quantum dynamical semigroup on a von Neumann algebra, we have constructed quantum random walks which converges strongly and the strong limit gives an Evans–Hudson dilation for the semigroup.

    • Author Affiliations

       

      Lingaraj Sahu1

      1. Stat-Math Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore 560 059, India

    • Dates

       
      Published
      August 2008
      Manuscript received
      30 May 2007
      Manuscript revised
      25 December 2007

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