Impact of Natural Turbulent Waters on Quantum Key Distribution: Temperature and Salinity Considerations

Quantum key distribution (QKD) has been identified as a viable solution for secure underwater communication. This study aims to characterize the impact of natural turbulent waters on systems. The performance of QKD systems is analyzed in terms of the quantum bit error rate and the secret key rate. We expand upon previous studies which only considered large separations by including large and small separations by comparing the turbulence length scale with the distance between two observation points. To that end, we obtain the analytical expression of the wave structure function (WSF) for small separation for propagating Gaussian beams. Since the WSF describes how the amplitude and phase of an optical wave change as it travels through the varying refractive index of the turbulent medium over a given distance, the accurate characterization remains essential in terms of revealing the beam wavefront distortion. Leveraging the practical parameters of underwater environment and communication systems, we demonstrate that the average temperature, average salinity concentration, temperature-salinity gradient, temperature and energy dissipation rates of turbulent water impact the performance and security of the QKD systems to a nonnegligible extent. It is also observed that the waters having high chlorophyll concentrations, e.g., coastal waters, drastically decrease the performance of the QKD systems due to strong absorption and scattering effects. The findings and insights gained from this study may help advance secure underwater communication, which in turn will aid in establishing future QKD networks. Potential applications of this research include secure underwater communication for defense, data gathering for marine environmental monitoring, remote data transmission, and deep-sea exploration.