Arithmetic Reconciliation for CVQKD With Gaussian Modulation

Abstract

We introduce a new and applicable technique for reconciling continuous-variable quantum key distribution (CVQKD) based on Gaussian modulation of coherent states. Its key feature is the application of the cumulative distribution function (CDF) to map Gaussian variables onto uniform <inline-formula> <tex-math notation="LaTeX">$[{0,1}]$ </tex-math></inline-formula> random variables, which are then expanded into Bernoulli <inline-formula> <tex-math notation="LaTeX">$(1/2)$ </tex-math></inline-formula> random variables, following the principles of Arithmetic Coding. This approach replaces the complex quantization procedures inherent in Slice Reconciliation, while also normalizing the variables of interest to generate the secret key, and thus avoiding the complexities associated with Multidimensional Reconciliation algorithms. The protocol does not use any post-selection, thus it can be proved secure against arbitrary collective attacks.