N-dimensional alternate coined quantum walks from a dispersion-relation perspective

Inbothitsstandardforms,thecoined[1]andthecontinuousone [2], quantum walk is the quantum version of a classicalrandom process, described by the diffusion and the teleg-rapher’s equations, respectively [3]. In the coined quantumwalk—the process we consider here—there is a system (thewalker)thatundergoesaconditionaldisplacement,totherightor the left, depending on the output of a