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Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

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Abstract

Open quantum walks (OQWs), originally introduced in Attal et al. (J Stat Phys 147(4):832–852, 2012), are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed in Pellegrini (J Stat Phys 154(3):838–865, 2014). These models, called continuous time open quantum walks (CTOQWs), appear as natural continuous time limits of discrete time OQWs. In particular, they are quantum extensions of continuous time Markov chains. This article is devoted to the study of homogeneous CTOQW on \(\mathbb {Z}^d\). We focus namely on their associated quantum trajectories which allow us to prove a central limit theorem for the “position” of the walker as well as a large deviation principle.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse UMR5219, CNRS, UPS IMT, Université de Toulouse, 31062, Toulouse Cedex 9, France

    Hugo Bringuier

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  1. Hugo Bringuier
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Correspondence to Hugo Bringuier.

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Communicated by Claude Alain Pillet.

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Bringuier, H. Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks. Ann. Henri Poincaré 18, 3167–3192 (2017). https://doi.org/10.1007/s00023-017-0597-7

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