Dynamical localization for d-dimensional random quantum walks

Dynamical localization for d-dimensional random quantum walks We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical localization holds for almost all random phases. This instance of Anderson localization implies that all quantum mechanical moments of the position operator are uniformly bounded in time and that spectral localization holds, almost surely. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Dynamical localization for d-dimensional random quantum walks

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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/s11128-012-0406-7
Publisher site
See Article on Publisher Site

Abstract

We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical localization holds for almost all random phases. This instance of Anderson localization implies that all quantum mechanical moments of the position operator are uniformly bounded in time and that spectral localization holds, almost surely.

Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 18, 2012

References

  • Disordered quantum walks in one lattice dimension
    Ahlbrecht, A.; Scholz, V.B.; Werner, A.H.
  • Asymptotic evolution of quantum walks with random coin
    Ahlbrecht, A.; Vogts, H.; Werner, A.H.; Werner, R.F.
  • Dynamical localization for unitary Anderson models
    Hamza, E.; Joye, A.; Stolz, G.

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