# Airborne Quantum Key Distribution Performance Analysis under Supersonic Boundary Layer
## 1 Introduction  
Quantum key distribution (QKD) is a promising technology to realize secure transmission, the fundamental principles of quantum mechanics guarantee the safety of QKD, which ensures the generation of information-theoretical-secure keys for distant users [1, 2, 3, 4, 5]. Furthermore, QKD can resist eavesdropping detection and tamper relying on physical principles, which has tremendous utilization potential in terms of finance, government, and military [6, 7]. Up to now, remarkable progress has been achieved both in fiber links [8, 9, 10, 11] and quantum satellites [12, 13, 14, 15, 16, 17, 18, 19]. However, the fundamental principles of quantum mechanics guarantee the safety of QKD, which ensures the generation of information-theoretical-secure keys for distant users [1, 2, 3, 4, 5]. Furthermore, QKD can resist eavesdropping detection and tamper relying on physical principles, which has tremendous utilization potential in terms of finance, government, and military [6, 7]. Up to now, remarkable progress has been achieved both in fiber links [8, 9, 10, 11] and quantum satellites [12, 13, 14, 15, 16, 17, 18, 19]. QKD systems, and gradually transferred from the laboratory to realistic applications. However, with constant orbits, limited communication time window and night-only quantum satellites, airborne [20, 21, 22, 23, 24, 25, 26, 27] platforms are ideal mobile nodes that can synergize with terrestrial links and quantum satellites to build the mobile, on-demand, and real-time coverage quantum network. For example, airborne quantum nodes could serve as temporary relays to solve the last-mile quantum key exchange for an inner-city or a field network benefiting from their rapid deployment capabilities. Several groups have reported their research in airborne quantum communications in recent years, the first demonstration was implemented in 2013, with the platform flying at the speed of 290 km/h and a height of 1.1 km [20]. In 2020, Nanjing University accomplished the first drone-based entanglement distribution [23] and achieved 200 m coverage and duration of 40 min, and in the next year,they expand the distance to 1000 m by means of one more drone [21] as an optical-relay. Compared to satellite quantum communication, airborne QKD features in high-speed maneuverability and suffers from the complicate atmosphere environment, including atmospheric turbulence, background noise and attitude disturbance, worse still, the boundary layer (BL) would also severely impact the quantum signal transmission. When the aircraft is flying at a high speed, usually larger than 0.3 Ma, a very thin layer of air will stick over the surface of the aircraft with high velocity, resulting in the BL, and it would introduce random disturbance to the transmitted photons, which would reduce the coupling efficiency and fidelity of quantum states [28], and decrease the performance of aircraft-based QKD. Currently, most implementations of airborne QKD only analyzed the noise from atmospheric turbulence and molecular scattering [25; 26], but ignored the boundary layer effects. In 2021, our group proposed an airborne QKD performance evaluation scheme that takes the boundary layer effect into account. The analysis results show that the aerodynamic optical effects caused by the boundary layer should be attended to, which will greatly reduce the final key rate [29]. In this article, an airborne QKD performance evaluation scheme with supersonic BL effect is proposed. We first simulate the density and refractive index field of the BL. Then, the photon propagation model in the boundary layer is established by performing the ray tracing method that uses the [PERSON] linear multistep method. In the end, we present the analysis results about the key rate of photons transmitted through the measured supersonic BL.