On a class of quantum channels, open random walks and recurrence

Abstract

We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combining open quantum random walks with a notion of recurrence, we are able to describe criteria for recurrence of the walk related to this class of channels. Positive recurrence for open walks is also discussed in this context.

18 pages, revised version

References in corpus (4)

• Open Quantum Random Walks
• Finding the Kraus decomposition from a master equation and vice versa
• The Generalized Lyapunov Theorem and its Application to Quantum Channels
• Radon-Nikodym derivatives of quantum operations

Cited by in corpus (21)

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• On period, cycles and fixed points of a quantum channel
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• Passage times, exit times and Dirichlet problems for open quantum walks
• Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
• Site recurrence of open and unitary quantum walks on the line
• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
• Quantum Markov chains: recurrence, Schur functions and splitting rules
• 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
• From open quantum walks to unitary quantum walks
• One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
• Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
• Dissipative realization of a quantum distance-based classifier using open quantum walks
• Nonhomogeneous quantum Markov chains and a notion of ergodicity
• Quantum Markov processes on graphs, monitoring and hitting times
• Open quantum random walks, hitting times, gambler's ruin and potential theory
• Homogeneous open quantum walks on the line: criteria for site recurrence and absorption