Haar-random coin quantum walks on d-regular graphs yield a non-ergodic averaged channel that depolarizes the coin while preserving forever-measurable initial-state information in the vertex subspace for Cayley graphs of Abelian groups.
Open Quantum Random Walks: Reducibility, Period, Ergodic Properties
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Quantum random walks on d-regular graphs with Haar-random coin operators
Haar-random coin quantum walks on d-regular graphs yield a non-ergodic averaged channel that depolarizes the coin while preserving forever-measurable initial-state information in the vertex subspace for Cayley graphs of Abelian groups.