Distribuição quântica de chaves com modulação não gaussiana: protocolos, desempenho e segurança.

Abstract

The quantum key distribution (QKD) protocols enable two geographically distant parties to share and generate random and unconditionally secure sequences, a task for which there is no classical counterpart and is made possible by the laws of quantum mechanics. In the recent decades, there has been interest in the development and study of protocols deőned by discrete (non-Gaussian) modulation of coherent states (DM-CVQKD, Discrete Modulated Continuous-Variable QKD), which are compatible with usual optical communications devices and architectures, allowing key distribution over existing optical networks. In this doctoral thesis, the efects resulting from the use of optimal schemes of discrete modulation on the performance and security of DM-CVQKD protocols will be analyzed. The őrst result shown is that, under the assumption of Gaussian collective attacks, modulation schemes that achieve the capacity of the Gaussian channel in classical communications exhibit analogous behavior when applied in DM-CVQKD protocols. In particular, the need for probabilistic shaping was identiőed for a discrete modulation scheme to have performance close to Gaussian modulation, as well as the non-uniform distribution of points in the complex plane for constellations with more than 232 points. Shifting attention to the compatibility between QKD protocols and the probabilistic shaping architecture of the constellation, the susceptibility of generating correlated symbols was discussed, and a reconciliation protocol was presented. Results were also developed relating the convergence of random variables to the convergence of density operators induced by these random variables. It was shown that the density operator representing a constellation weakly converges to the thermal state if the sequence of random variables representing the constellation converges in distribution to the normal distribution. Consequently, the łnon-Gaussianityž of the constellation approaches zero as the cardinality of the constellation increases, as well as the diference between the key rates of the non-Gaussian modulation protocol and its Gaussian counterpart, providing assurance that the lower bound commonly used in security proofs is fair if the constellation is large enough. Finally, three propositions are presented regarding the convergence (in trace norm) of coherent state constellations: a bound for the approximation error through dimension reduction of the Hilbert space (energy test), the convergence of the spectrum of eigenvalues and eigenvectors, and the convergence of the puriőcation of the coherent state constellation.