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Dynamical localization for d-dimensional random quantum walks

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A Publisher's Erratum to this article was published on 22 June 2012

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.

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Authors and Affiliations

  1. UJF-Grenoble 1, CNRS Institut Fourier UMR 5582, Grenoble, 38402, France

    Alain Joye

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  1. Alain Joye
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Correspondence to Alain Joye.

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Partially supported by the Agence Nationale de la Recherche, grant ANR-09-BLAN-0098-01.

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Joye, A. Dynamical localization for d-dimensional random quantum walks. Quantum Inf Process 11, 1251–1269 (2012). https://doi.org/10.1007/s11128-012-0406-7

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