  The communication capacity of Gaussian bosonic channels with memory has
recently attracted much interest. Here, we investigate a method to prepare the
multimode entangled input symbol states for encoding classical information into
these channels. In particular, we study the usefulness of a Gaussian matrix
product state (GMPS) as an input symbol state, which can be sequentially
generated although it remains heavily entangled for an arbitrary number of
modes. We show that the GMPS can achieve more than 99.9% of the Gaussian
capacity for Gaussian bosonic memory channels with a Markovian or non-Markovian
correlated noise model in a large range of noise correlation strengths.
Furthermore, we present a noise class for which the GMPS is the exact optimal
input symbol state of the corresponding channel. Since GMPS are ground states
of particular quadratic Hamiltonians, our results suggest a possible link
between the theory of quantum communication channels and quantum many-body
physics.
