Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has such high noise levels that the error-correcting code must have very low rate. In this regime it becomes feasible to implement random-codebook error correction, which is known to perform close to capacity. We propose a reverse reconciliation scheme for CVQKD in which the first step is advantage distillation based on random-codebook error correction operated above the Shannon limit. Our scheme has a novel way of achieving statistical decoupling between the public reconciliation data and the secret key. We provide an analysis of the secret key rate for the case of Gaussian collective attacks, and we present numerical results. The best performance is obtained when the message size exceeds the mutual information $I(X;Y)$ between Alice's quadratures $X$ and Bob's measurements $Y$, i.e. the Shannon limit. This somewhat counter-intuitive result is understood from a tradeoff between code rate and frame rejection rate, combined with the fact that error correction for QKD needs to reconcile only random data. We obtain secret key rates that lie far above the Devetak-Winter value $I(X;Y) - I(E;Y)$, which is the upper bound in the case of one-way error correction. Furthermore, our key rates lie above the PLOB bound for Continuous-Variable detection, but below the PLOB bound for Discrete-Variable detection.

翻译：在长距离连续变量量子密钥分发（CVQKD）中，噪声水平极高，导致纠错码必须采用极低的码率。在此条件下，实现接近容量的随机码本纠错成为可能。我们提出一种适用于CVQKD的反向协调方案，其第一步是基于香农极限以上运行的随机码本纠错进行优势提取。该方案通过新颖方式实现公开协调数据与密钥之间的统计解耦。我们针对高斯集体攻击情形进行了密钥率分析，并给出了数值结果。最佳性能出现在消息规模超过Alice的象限X与Bob的测量Y之间的互信息$I(X;Y)$（即香农极限）时。这一略显反直觉的结果源于码率与帧拒绝率之间的权衡，且QKD纠错仅需协调随机数据。我们获得的密钥率远超Devetak-Winter值$I(X;Y) - I(E;Y)$（该值为单向纠错情况下的理论上限），同时高于连续变量检测的PLOB界限，但低于离散变量检测的PLOB界限。