Homogeneous Open Quantum Random Walks on a lattice
Résumé
We study Open Quantum Random Walks for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. Using the results recently obtained by Attal et al. (Ann. Henri Poincaré, 2014), 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, and an ergodic result for the state process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space $h={\mathbb C}^2$.