  We study the light-cone velocity for global quenches in the non-interacting
XY chain starting from a class of initial states that are eigenstates of the
local $z$-component of the spin. We point out how translation invariance of the
initial state can affect the maximal speed at which correlations spread. As a
consequence the light-cone velocity can be state-dependent also for
non-interacting systems: a new effect of which we provide clear numerical
evidence and analytic predictions. Analogous considerations, based on numerical
results, are drawn for the evolution of the entanglement entropy.
