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In this work we make use of generalized inverses associated with quantumchannels acting on finite-dimensional Hilbert spaces, so that one may calculatethe mean hitting time for a particle to reach a chosen goal subspace. Thequestions studied in this work are motivated by recent results on quantumdynamics on graphs, most particularly quantum Markov chains. We focus ondescribing how generalized inverses and hitting times can be obtained, with themain novelties of this work with respect to previous ones being that a) we areable to weaken the notion of irreducibility, so that reducible examples can beconsidered as well, and b) one may consider arbitrary arrival subspaces forgeneral positive, trace preserving maps. Natural examples of reducible maps aregiven by unitary quantum walks. We also take the opportunity to explain how amore specific inverse, namely the group inverse, appears in our context, inconnection with matrix algebraic constructions which may be of independentinterest.

Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks