  We consider a d-dimensional random quantum walk with site-dependent random
coin operators. The corresponding transition coefficients are characterized by
deterministic amplitudes times independent identically distributed
site-dependent random phases. When the deterministic transition amplitudes are
close enough to those of a quantum walk which forbids propagation, we prove
that dynamical localization holds for almost all random phases. This instance
of Anderson localization implies that all quantum mechanical moments of the
position operator are uniformly bounded in time and that spectral localization
holds, almost surely.
