Passage times, exit times and Dirichlet problems for open quantum walks

Abstract

We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the expectation of that passage time, and the expectation of the number of visits, and discuss the notion of recurrence for open quantum walks. We also study exit times and exit probabilities from a finite domain, and use them to solve Dirichlet problems and to determine harmonic measures. We consider in particular the case of irreducible open quantum walks. The results we obtain extend those for classical Markov chains.

References in corpus (2)

• Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
• Site recurrence of open and unitary quantum walks on the line

Cited by in corpus (8)

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• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
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• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem
• Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics
• Mean hitting times of quantum Markov chains in terms of generalized inverses