Gaussian matrix-product states for coding in bosonic communication channels

TL;DR

This paper demonstrates that Gaussian matrix product states can nearly achieve the maximum capacity for Gaussian bosonic channels with memory, offering a practical method for encoding classical information in quantum communication.

Contribution

The study introduces GMPS as an effective and near-optimal input state for bosonic channels with memory, linking quantum communication with many-body physics.

Findings

GMPS achieve over 99.9% of the Gaussian capacity.

GMPS are the exact optimal states for certain noise classes.

Results apply to both Markovian and non-Markovian noise models.

Abstract

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.