Removing correlations in signals transmitted over a quantum memory channel

We consider a model of a bosonic memory channel, which induces correlations among the transmitted signals. The application of suitable unitary transformations at the encoding and decoding stages allows the complete removal of correlations, thereby mapping the memory channel into a memoryless one. However, such transformations, being global over an arbitrarily large number of bosonic modes, are not realistically implementable. We then introduce a family of efficiently realizable transformations, which can be used to partially remove correlations among errors, and we quantify the reduction of the gap with memoryless channels.