Pretty good state transfer in discrete-time quantum walks

Abstract We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that is characterized by spectrum certain Hermitian adjacency matrix graph; more specifically, vertices involved must be strongly cospectral relative to this matrix, and arccosines its eigenvalues satisfy some number theoretic conditions. Using normalized matrices, cyclic covers, on linear relations between geodetic angles, construct several infinite families walks exhibits phenomenon.