  We consider the dynamics of the quantum XY chain with disorder under the
general assumption that the expectation of the eigenfunction correlator of the
associated one-particle Hamiltonian satisfies a decay estimate typical of
Anderson localization. We show that, starting from a broad class of product
initial states, entanglement remains bounded for all times. For the XX chain,
we also derive bounds on the particle transport which, in particular, show that
the density profile of initial states that consist of fully occupied and empty
intervals, only have significant dynamics near the edges of those intervals,
uniformly for all times.
