Secret key extraction in direct reconciliation CV-QKD systems

Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.