  The notion of forgetfulness, used in discrete quantum memory channels, is
slightly weakened in order to be applied to the case of continuous channels.
This is done in the context of quantum memory channels with Markovian noise. As
a case study, we apply the notion of weak-forgetfulness to a bosonic memory
channel with additive noise. A suitable encoding and decoding unitary
transformation allows us to unravel the effects of the memory, hence the
channel capacities can be computed using known results from the memoryless
setting.
