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

In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach chosen goal subspace. The questions studied in are motivated by recent results dynamics graphs, most particularly Markov chains. We focus describing how and times can be obtained, main novelties respect previous ones being (a) able weaken notion irreducibility, reducible examples considered as well, (b) consider arbitrary arrival subspaces general positive, trace-preserving maps. Natural maps given unitary walks. also take opportunity explain more specific inverse, namely group appears our context, connection matrix algebraic constructions which independent interest.