  Quantum communication theory sets the maximum rates at which information can
be encoded and decoded reliably given the physical properties of the
information carriers. Here we consider the problem of readout of a digital
optical memory, where information is stored by means of the optical properties
of the memory cells that are in turn probed by shining a laser beam on them.
Interesting features arise in the regime in which the probing light has to be
treated quantum mechanically. The maximum rate of reliable readout defines the
quantum reading capacity, which is proven to overcome the classical reading
capacity, obtained by probing with classical light, in several relevant
settings. We consider a model of optical memory in which information is encoded
in the (complex-valued) attenuation factor and study the effects on the reading
rates of thermal and correlated noise. The latter type of noise arises when the
effects of wave diffraction on the probing light beam are taken into account.
We discuss the advantages of quantum reading over the classical one and show
that the former is substantially more robust than the latter under thermal
noise in the regime of low power per pulse.
