Homogeneous open quantum random walks a lattice

Abstract. We study open quantum random walks (OQRW) for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. Using the results obtained recently in [5], we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space h = C2. 1

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