  Given a discrete reversible dynamics, we can define a quantum dynamics, which
acts on basis states like the classical one, but also allows for superpositions
of them. It is a curious fact that in the quantum version, local changes in the
initial state, after a single dynamical step, can sometimes can be detected
much farther away than classically. Here we show that this effect is no use for
generating faster signals. In a run of many steps the quantum propagation
neighborhood can only increase by a constant fringe, so there is no asymptotic
increase in speed.
