Homogeneous Open Quantum Random Walks on a lattice

Abstract

We study Open Quantum Random Walks for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. We consider 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 $h={\mathbb{C}}^2$.

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• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
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• Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs
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• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements