Continuous-Variable QKD with key rates far above Devetak-Winter

Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has such high noise levels that the employed error-correcting codes 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 random-codebook reverse reconciliation scheme for CVQKD that is inspired by spread-spectrum watermarking. Our scheme has a novel way of achieving statistical decoupling between the publicly sent reconciliation data and the secret key. We provide a theoretical analysis of the secret key rate and we present numerical results. The best performance is obtained when the message size exceeds the mutual information I(X;Y) between Alice and Bob's measurements. 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 lengths that lie far above the Devetak-Winter value I(X;Y)-I(E;Y).