Coherent-state constellations and polar codes for thermal Gaussian channels

TL;DR

This paper develops efficient encoding schemes for thermal Gaussian channels using polar codes and coherent state constellations, achieving classical capacity and Gaussian coherent information for classical and quantum data transmission.

Contribution

It introduces a novel coding scheme combining polar codes with coherent state constellations to approach the channel capacities practically.

Findings

Codes achieve classical capacity for thermal channels

Encoding can be implemented with linear optics

Approach is efficient and practical for quantum communication

Abstract

Optical communication channels are ultimately quantum-mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite "constellation" of coherent states. Encoding of classical information can be done using linear optics.