Capacities of lossy bosonic channel with correlated noise

We evaluate the information capacities of a lossy bosonic channel with correlated noise. The model generalizes the one recently discussed by Pilyavets et al (2008 Phys. Rev. A 77 052324), where memory effects come from the interaction with correlated environments. Environmental correlations are quantified by a multimode squeezing parameter, which vanishes in the memoryless limit. We show that a global encoding/decoding scheme, which involves input-entangled states among different channel uses, is always preferable with respect to a local one in the presence of memory. Moreover, in a certain range of the parameters, we provide an analytical expression for the classical capacity of the channel showing that a global encoding/decoding scheme allows it to be attained. All the results can be applied to a broad class of bosonic Gaussian channels.