Limit theorems for open quantum random walks

Abstract

We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schrödinger-Heisenberg representation in quantum mechanics. By this, we can compute the distribution of the open quantum random walks concretely for many examples and thereby we can also obtain the limit distributions of them. In particular, it is possible to get rid of the initial state when we consider the evolution of the walk, it appears only in the last step of the computation.

References in corpus (4)

• Quantum walks: a comprehensive review
• Decoherence in quantum walks - a review
• Open Quantum Random Walks
• Open Quantum Walks on Graphs

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