Central limit theorem for reducible and irreducible open quantum walks

Abstract

In this work we aim at proving central limit theorems for open quantum walks on ${\mathbb{Z}}^d$. We study the case when there are various classes of vertices in the network. Furthermore, we investigate two ways of distributing the vertex classes in the network. First we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a uniform distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.

20 pages, 4 figures

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• Central limit theorems for open quantum random walks on the crystal lattices
• Limit properties of global interaction stochastic quantum walks on directed graphs
• Mean hitting times of quantum Markov chains in terms of generalized inverses
• From open quantum walks to unitary quantum walks
• Quantum walks on hypergraphs
• A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks
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