Coherent state constellations for Bosonic Gaussian channels

Abstract

We propose constellations of finitely-many coherent states for high-rate quantum and classical communication over the thermal noise Bosonic Gaussian channel. Our constructions are based on constellations for the classical additive white Gaussian noise (AWGN) channel, and we adapt the results of Wu and Verdu [Allerton 2010, pp. 620] for the AWGN to determine achievable rates of classical and quantum information transmission for the thermal noise channel. Several constellations allow classical rates approaching the classical capacity, recently determined by Giovannetti et al. [Nature Photonics 8, 796 (2014)], while in the quantum case the rates approach the Gaussian coherent information. The constellations can also be used for private transmission of classical information at the coherent information rate.