On a Generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks

Abstract We consider homogeneous open quantum walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of trajectories walk. prove that properly rescaled asymptotically approaches mixture Gaussian measures. can generalize existing central limit type results give more explicit expressions for involved asymptotic quantities, dropping any additional condition use deformation spectral techniques, together reducibility properties channel associated Further, provide large deviation principle case fast recurrent at least lower upper bounds general case.