Continuous-Variable Quantum Key Distribution with key rates far above the PLOB bound

Abstract

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.