Monte Carlo-based security analysis for multi-mode continuous-variable quantum key distribution over underwater channel

With the booming development and application of ocean exploration and investigation, it has become more and more important to achieve underwater communications for the establishment of global networks. This paper deals with a Monte Carlo-based performance analysis on multi-mode continuous-variable quantum key distribution over underwater links, where Monte Carlo model can characterize the complex probability density of underwater components. Compared with previous studies carried out in single-mode setting, the multi-mode protocol admits higher secret key rate. Last but not least, using non-Gaussian operations, we further improve the performance of multi-mode protocol, since it increases and distills entanglement in Gaussian entangled states.