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Reconciliation with polar codes by Gaussian approximation for continuous-variable quantum key distribution

In quantum key distribution, reconciliation refers to a post process that extracts two equal binary strings from quantum raw keys between two authenticated parties before distillation of secret keys via privacy amplification. In continuous-variable quantum key distribution (CV-QKD) where coherent states of light are used instead of single photons [1], this is important because it is harder for them to extract and share the same binary strings from continuous variables relative to an eavesdropper. To quantify its performance, reconciliation efficiency is defined as β = R C , where R denotes code rate and C indicates Shannon’s channel capacity. Reconciliation efficiency close to unity at the low signal-to-noise ratio (SNR) regime is a necessary condition to increase the transmission distance of secret keys.