Underwater quantum communication is of great significance to seabed exploration and global communication, whose quality is affected by the complex and changeable marine environment. The stable and high-quality transmission of optical quantum signals can ensure the accurate transmission of information. In the process of underwater quantum communication transmission, various marine environmental factors will inevitably lead to the attenuation of communication links, such as seawater molecules, algal suspended particles, and marine sediment particles. However, up to now, research on the effect of marine non-pigment agglomerated particles on the performance of underwater quantum channels has not been carried out. Non-pigment suspended particles in seawater mainly include suspended sediment particles, mineral particles, and excreta of marine organisms. During underwater quantum communication, the collision between non-pigment agglomerated particles and light quantum signals will cause the attenuation of optical signals, which can lead to the attenuation of communication links and reduce the reliability of underwater quantum communication. It is expected that the simulation results in this study can provide a reference for the design and optimization of quantum communication systems in the marine environment.

Marine non-pigment suspended particles are agglomerated particle systems formed by multiple single particles. After linear superposition approximation treatment for marine non-pigment agglomerated particles of different sizes, they can still be regarded as spherical particles, similar to equivalent spheres. Firstly, Mie scattering theory and the Gordon model are used to analyze the absorption and scattering characteristics of marine non-pigment agglomerated particles. Then, the relationship model between mass concentration of marine non-pigment agglomerated particles and link attenuation is built, and simulation experiments are carried out. After that, a physical model for the quantum security key generation rate under the influence of marine non-pigment agglomerated particles is constructed, and the simulation experiment is conducted for the preparation and measurement quantum key distribution system. For quantum communication networks based on entangled states, the influence of marine non-pigment agglomerated particles on the establishment rate of underwater quantum channels is studied and analyzed. In addition, the capacity of the amplitude damping channel in a marine non-pigment environment is analyzed and calculated.

For the same wavelength, the Mie scattering coefficient of marine non-pigment agglomerated particles is proportional to the mass concentration; for the same mass concentration, a shorter incident wavelength means a greater scattering coefficient. Moreover, the absorption coefficient of marine non-pigment agglomerated particles is exponentially related to the incident wavelength (Fig. 1). The link attenuation decreases with the increase in the wavelength of the incident light signal, and a larger mass concentration of marine non-pigment agglomerated particles is accompanied by a more significant decreasing trend of the quantum link attenuation (Fig. 2). When the optical signal wavelength is constant, the link attenuation shows an upward trend with the increase in the mass concentration of non-pigment agglomerated particles (Fig. 3). The generation rate of the quantum security key grows with the increase in the wavelength of the incident light signal and drops with the increase in the mass concentration of marine non-pigment agglomerated particles (Fig. 4). The establishment rate of quantum channels is greatly affected by fidelity. For the same fidelity, the establishment rate increases with the increase in the wavelength of the incident optical signal, but the overall upward trend is gentle (Fig. 6). The capacity of the amplitude damping channel shrinks with the increase in the mass concentration and transmission distance of marine non-pigment agglomerated particles (Fig. 9). Overall, a higher incident wavelength indicates better quality of underwater quantum communication when only marine non-pigment agglomerated particles are considered.

In the present study, the scattering and absorption characteristics of non-pigment agglomerated particles are analyzed according to the Mie scattering theory and the Gordon model. For different wavelengths of optical signals, the relationship models between mass concentration of marine non-pigment agglomerated particles and link attenuation, generation rate of the quantum security key, channel establishment rate, as well as the capacity of the amplitude damping channel are constructed and simulated. The experimental results show that for quantum communication using 510-nm optical signals, the link attenuation increases from 2.562 to 13.100 when the mass concentration of non-pigment agglomerated particles increases from 0 to 3 mg/L. When 580-nm wavelength signals are selected as the incident wavelength, the mass concentration of non-pigment agglomerated particles is 1.2 mg/L, and the transmission distance increases from 0 to 2 km, while the generation rate of the quantum security key increases from 2.17×10^-4 to 8.30×10^-5. When 540-nm optical signals are used for underwater quantum communication, and the fidelity increases from 0.60 to 0.99, the quantum channel establishment rate is attenuated from 93.61 to 7.39 pair/s. For underwater quantum communication with 580-nm optical signals, when the mass concentration of non-pigment agglomerated particles is 1.8 mg/L, and the transmission distance increases from 0.5 to 10 km, the channel capacity decreases from 0.726 to 0.040. When the transmission distance is greater than 7 km, and the mass concentration is greater than 2.1 mg/L, the capacity of the amplitude damping channel is less than 0.069, and the communication efficiency is extremely low.