Memory effects in attenuation and amplification quantum processes

With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable with the typical relaxation time of the channel environment. We then introduce a model of 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.