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.
BARC codes: general polynomial framework for coherent-state superposition codes
Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（先进智能与计算研究所，科学、技术与研究局）；Singapore University of Technology and Design（新加坡科技设计大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院南洋量子枢纽）
Security bounds for unidimensional discrete-modulated CV-QKD: a Gaussian extremality approach
QuIIN - Quantum Industrial Innovation, EMBRAPII CIMATEC Competence Center in Quantum Technologies, SENAI CIMATEC（QuIIN - 量子工业创新，EMBRAPII CIMATEC 量子技术能力中心，SENAI CIMATEC）；Instituto de Fı́sica, Universidade Federal do Rio de Janeiro（物理研究所，里约热内卢联邦大学）；Department of Electrical and Photonics Engineering, Technical University of Denmark（电气与光子工程系，丹麦技术大学）
