Modulation variance optimization in discrete modulated CV-QKD systems

The distribution of symmetric keys over optical networks is possible through the implementation of continuous variables quantum key distribution (CV-QKD) systems. Despite the rate of key extraction in CV-QKD being maximized for Gaussian modulation (GM), its practical implementation is demanding due to the finite extinction ratio of the electro-optic modulators. The use of discrete modulation (DM) allows for a simpler practical implementation. Provided that higher-order constellations can be used, DM can approximate the performances of GM. Higher-order DM has been shown to be feasible experimentally in CV-QKD. Notwithstanding, such implementations are usually obtained in offline without applying all the post-processing steps, particularly the information reconciliation, turning the validity of the results dependent on a null frame error rate after information reconciliation. Besides that, a fixed value is typically assumed for the reconciliation efficiency value, being the modulation variance optimized under such assumptions. This disregarding the dependency of the reconciliation efficiency parameter on the method for information reconciliation and on the modulation variance. In this work we study the impact that such assumptions have on the optimization of the modulation variance in a CV-QKD system using probabilistic shaped higher-order DM. Moreover, we analyse how optimizing the modulation variance can affect the extraction key rates of symmetric keys at the output of the CV-QKD system. Besides the assumptions of null frame error rate and of the reconciliation efficiency, we study how different code rates may also affect the optimization of the modulation variance. This considering M-symbol quadrature amplitude modulation and multidimensional reconciliation.