Random coding for long-range continuous-variable QKD

Quantum Key Distribution (QKD) schemes are key exchange protocols based on the physical properties of quantum channels. They avoid the computational-hardness assumptions that underlie the security of classical key exchange. Continuous-Variable QKD (CVQKD), in contrast to qubit-based discrete-variable (DV) schemes, makes use of quadrature measurements of the electromagnetic field. CVQKD has the advantage of being compatible with standard telecom equipment, but at long distances has to deal with very low signal to noise ratios, which necessitates labour-intensive error correction. It is challenging to implement the error correction decoding in realtime. In this paper we introduce a random-codebook error correction method that is suitable for long range Gaussian-modulated CVQKD. We use likelihood ratio scoring with block rejection based on thresholding. For proof-technical reasons, the accept/reject decisions are communicated in encrypted form; in this way we avoid having to deal with non-Gaussian states in the analysis of the leakage. The error correction method is highly parallelisable, which is advantageous for realtime implementation. Under conservative assumptions on the computational resources, we predict a realtime key ratio of at least 8% of the Devetak-Winter value, which outperforms existing reconciliation schemes.