  We address memory effects and diffusive properties of a continuous-time
quantum walk on a one-dimensional percolation lattice affected by spatially
correlated random telegraph noise. In particular, by introducing spatially
correlated time-dependent fluctuations in nearest-neighbor hopping amplitudes,
we describe random domains characterized by global noise. The resulting open
dynamics of the walker is then unraveled by an ensemble average over all the
noise realizations. Our results show that time-dependent noise assisted by
spatial correlations leads to strong memory effects in the walker dynamics and
to robust diffusive behavior against the detrimental action of uncorrelated
noise. We also show that spatially correlated classical noise enhances
localization breaking, thus making a quantum particle spread on longer
distances across the lattice.
