  We study quantum-state transfer in $XX$ spin-$1/2$ chains where both
communicating spins are weakly coupled to a channel featuring disordered
on-site magnetic fields. Fluctuations are modelled by long-range correlated
sequences with self-similar profile obeying a power-law spectrum. We show that
the channel is able to perform an almost perfect quantum-state transfer in most
of the samples even in the presence of significant amounts of disorder provided
the degree of those correlations is strong enough. In that case, we also show
that the lack of mirror symmetry does not affect much the likelihood of having
high-quality outcomes. Our results advance a further step in designing robust
devices for quantum communication protocols.
