In continuous-variable quantum key distribution, information reconciliation is required to extract a shared secret key from correlated random variables obtained through the quantum channel. Reverse reconciliation (RR) is generally preferred, since the eavesdropper has less information about Bob's measurements than about Alice's transmitted symbols. When discrete modulation formats are employed, however, soft information is available only at Bob's side, while Alice has access only to hard information (her transmitted sequence). This forces her to rely on hard-decision decoding to recover Bob's key. In this work, we introduce a novel RR technique for PAM (and QAM) in which Bob discloses a carefully designed soft metric to help Alice recover Bob's key, while leaking no additional information about the key to an eavesdropper. We assess the performance of the proposed technique in terms of achievable secret key rate (SKR) and its bounds, showing that the achievable SKR closely approaches the upper bound, with a significant gain over hard-decision RR. Finally, we implement the scheme at the coded level using binary LDPC codes with belief-propagation decoding, assess its bit-error rate through numerical simulations, compare the observed gain with theoretical predictions from the achievable SKR, and discuss the residual gap.

翻译：在连续变量量子密钥分发中，信息协调是从量子信道获得的关联随机变量中提取共享密钥的必要步骤。逆向协调通常更受青睐，因为窃听者对Bob测量结果的了解少于对Alice发送符号的了解。然而，当采用离散调制格式时，仅Bob端可获得软信息，而Alice仅能获取硬信息（即其发送序列）。这迫使Alice必须依赖硬判决译码来恢复Bob的密钥。本文提出了一种适用于PAM（及QAM）调制的新型逆向协调技术：Bob向Alice公开一种精心设计的软度量以协助其恢复Bob的密钥，同时确保该过程不会向窃听者泄露任何额外的密钥信息。我们通过可达到的密钥生成率及其界限评估了所提技术的性能，结果表明可达到的密钥生成率可逼近理论上界，且较硬判决逆向协调获得显著增益。最后，我们在编码层面采用基于置信传播译码的二进制LDPC码实现了该方案，通过数值仿真评估了其误码率，将观测到的增益与可达到密钥生成率的理论预测值进行对比，并讨论了残余差距。