  We prove maximal speed estimates for nonlinear quantum propagation in the
context of the Hartree equation. More precisely, under some regularity and
integrability assumptions on the pair (convolution) potential, we construct a
set of energy and space localized initial conditions such that, up to
time-decaying tails, solutions starting in this set stay within the light cone
of the corresponding initial datum. We quantify precisely the light cone speed,
and hence the speed of nonlinear propagation, in terms of the momentum of the
initial state.
