In recent years, quantum communication has become a research hotspot in China and abroad for its better data transmission security. As the core of the quantum information theory, quantum communication can be more secure and reliable for information transmission and is an important direction of inquiry. With the development of underwater wireless communication, it is important to research underwater quantum communication for marine and military fields. Bubbles are ubiquitous in the ocean, and the scattering and refraction effects of bubbles on light can cause certain losses in optical quantum transmission, which exerts a certain impact on the performance of underwater optical quantum communication. However, the research on the effect of bubbles on the channel performance of underwater quantum communication has not been conducted. By building the particle size distribution and scattering coefficient models of marine bubbles, the paper analyzes the effects of different condition parameters on link attenuation, entanglement, channel capacity, and channel bit error rate (BER) in the marine bubble environment to investigate the influence of these bubbles on the channel performance of underwater quantum communication. This is of great significance to improve the efficiency of underwater quantum communication.

Marine bubbles are mainly generated by wind-driven wave breaking. With an aim to study the influence of marine bubbles on the channel performance of underwater quantum communication, the particle size distribution function of the bubbles is firstly derived and established. The scattering characteristics and extinction coefficient of the bubbles are studied according to the particle size distribution model of marine bubbles. Additionally, according to the extinction characteristics, the relationship between marine bubble parameters and link attenuation is firstly established, and then the effects of different depths and bubble radii on channel entanglement are analyzed. Then, the effects of different bubble concentrations and transmission distances on three channel capacities of amplitude damped channel, depolarized channel, and bit-flip channel are analyzed respectively. Finally, the effects of different bubble concentrations and transmission distances on channel BER are studied and analyzed. At the same time, the effects of different bubble concentrations and transmission distances on the channel BER are studied and simulated. The theoretical analysis and simulation results can provide a reference for the design of underwater quantum communication in the marine bubble environment.

The simulation results show that the density of bubbles decreases with the increasing depth from the sea level, whereas increases with the rising wind speed. The scattering coefficient of bubbles has the same trend as the bubble density number under the same parameter conditions. Under short transmission distance and small bubble concentration, the link attenuation caused by marine bubbles is also small. With the increase in the transmission distance of optical quantum signals and the bubble concentration, the link attenuation grows rapidly. The channel entanglement increases with the rising depth from the sea level and the decreasing bubble radius. For the amplitude damping channel, depolarization channel, and bit-flip channel, the channel capacity decreases to different degrees with the increasing transmission distance and bubble concentration. The capacity of the depolarization channel and the bit-flip channel is more affected by the transmission distance, and the transmission distance exerts less effect on the channel capacity. The BER in the marine bubble environment is also affected by the transmission distance and bubble concentration. When the bubble concentration is small with a short transmission distance, the system BER changes slowly. When the bubble concentration is large with a long transmission distance, the optical quantum signal attenuates seriously and the BER value rises rapidly.

To investigate the effect of marine bubbles on the channel performance of underwater quantum communication, this paper studies the scattering characteristics of the bubbles according to the particle size distribution model of marine bubbles. In addition, the effects of different condition parameters on link attenuation, entanglement, channel capacity, and channel BER are analyzed according to the extinction coefficient of bubbles, and simulation experiments are conducted. The results show that the increase in bubble concentration and transmission distance increases the link attenuation and BER, and the channel capacity decreases for amplitude damping channel, depolarization channel, and bit-flip channel. The channel entanglement decreases with the increasing bubble radius and decreasing depth, and the impact of marine bubbles on communication performance cannot be ignored. Meanwhile, parameters related to underwater quantum communication should be adjusted appropriately according to the concentration of marine bubbles to reduce the impact of the marine bubble environment on the communication system and improve the reliability of the communication system in practical application.