Distribution Statistics and Random Matrix Formalism of Multicarrier Continuous-Variable Quantum Key Distribution

Abstract: We propose a combined mathematical framework of order statistics and random matrix theory for multicarrier continuous-variable (CV) quantum key distribution (QKD). In a multicarrier CVQKD scheme, the information is granulated into Gaussian subcarrier CVs, and the physical Gaussian link is divided into Gaussian sub-channels. The sub-channels are dedicated to the conveying of the subcarrier CVs. The distribution statistics analysis covers the study of the distribution of the sub-channel transmittance coefficients in the presence of a Gaussian noise and the utilization of the moment generation function (MGF) in the error analysis. We reveal the mathematical formalism of sub-channel selection and formulation of the transmittance coefficients, and show a reduced complexity progressive sub-channel scanning method. We define a random matrix formalism for multicarrier CVQKD to evaluate the statistical properties of the information flowing process. Using random matrix theory, we express the achievable secret key rates and study the efficiency of the AMQD-MQA (adaptive multicarrier quadrature division-multiuser quadrature allocation) multiple-access multicarrier CVQKD. The proposed combined framework is particularly convenient for the characterization of the physical processes of experimental multicarrier CVQKD.