Security of quantum communications in oceanic turbulence

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.