The channel fading induced in the ocean quantum links is a major obstacle restricting the performance of ocean quantum key distribution. To determine the ultimate limits at which secret bits (and entanglement) can be distributed via a seawater medium, we propose an analytical model for ocean quantum links to derive the probability distribution of the transmittance, which characterizes the evolution of the quantum state over the fading channel. The proposed model includes the effects of absorption, scattering, turbulence, and ocean thermal noise due to background light. Our comprehensive numerical analysis of several practical scenarios encompasses both pure-loss bounds and thermal-loss bounds, with a submarine at various depths and in various oceans on earth. Besides identifying ultimate limits, we present a security analysis of coherent-state and squeezed-state protocols, showing the secret key rate of both the asymptotic case and finite-size regimes.

We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the eight-state protocol in asymptotic and finite-size cases is analyzed in detail. Simulation results illustrate that the more complex is the seawater composition, the worse is the performance of the protocol. For different types of seawater channels, we can improve the performance of the protocol by selecting different optimal modulation variances and controlling the extra noise on the channel. Besides, we can find that the performance of the eight-state protocol is better than that of the four-state protocol, and there is little difference between homodyne detection and heterodyne detection. Although the secret key rate of the protocol that we propose is still relatively low and the maximum transmission distance is only a few hundred meters, the research on CV-QKD over the seawater channel is of great significance, which provides a new idea for the construction of global secure communication network.

The current investigation on continuous-variable quantum key distribution (CV-QKD) is mainly based on the optical fibre or the free space atmosphere channel, while the ocean, which covers most of the Earth, has not been well utilized. In this paper, we analyze the influence of depth and wavelength on the attenuation effect of seawater on light by using a model based on the concentration of chlorophyll-a, and propose an improved four-state underwater CV-QKD protocol with a heralded hybrid linear amplifier (HLA). Both homodyne detection with a phase-sensitive amplifier and heterodyne detection with a phase-insensitive amplifier are considered. Simulation results show that the introduction of the heralded HLA can effectively extend the secure transmission distance of the key. Besides, when the transmission distance is relatively long, the secret key rate of the protocol is higher than that of the protocol without HLA.

Phase drift extremely limits the secure key rate and secure transmission distance, which is non-negligible in local oscillation continuous variable quantum key distribution (LLO CV-QKD). In order to eliminate the impact caused by phase drift, we analyze the phase noise of the system and propose a phase compensation method based on convolutional neural network (CNN). Moreover, the compensation is performed on the signal according to the estimated value of phase drift before coherent detection. In numerical simulation, we compare the performance of phase compensation methods based on CNN and Kalman filter (KF), and the results show that CNN-based phase compensation has higher accuracy and stability.