  With increasing communication rates via quantum channels, memory effects
become unavoidable whenever the use rate of the channel is comparable to the
typical relaxation time of the channel environment. We introduce a model of a
bosonic memory channel, describing correlated noise effects in quantum-optical
processes via attenuating or amplifying media. To study such a channel model,
we make use of a proper set of collective field variables, which allows us to
unravel the memory effects, mapping the n-fold concatenation of the memory
channel to a unitarily equivalent, direct product of n single-mode bosonic
channels. We hence estimate the channel capacities by relying on known results
for the memoryless setting. Our findings show that the model is characterized
by two different regimes, in which the cross correlations induced by the noise
among different channel uses are either exponentially enhanced or exponentially
reduced.
