Risk-Sensitive Stochastic Control for Robust UAV-Assisted Free-Space Quantum Key Distribution under Atmospheric Turbulence

Unmanned aerial vehicles (UAVs) enable rapidly deployable secure communication, while quantum key distribution (QKD) ensures information-theoretic security over free-space optical channels. In UAV-assisted QKD, however, atmospheric turbulence and mobility-induced misalignment introduce stochastic channel fluctuations that cause intermittent secrecy degradation. Existing trajectory optimization methods are largely deterministic or risk-neutral and fail to address rare but severe deep-fading events. We develop a risk-sensitive stochastic control framework for robust UAV-assisted free-space QKD under atmospheric uncertainty. The UAV motion is modeled as a continuous-time stochastic dynamical system, and the quantum channel transmissivity is characterized by mobility-dependent log-normal fading, yielding a stochastic secret key rate process. The exponential performance functional simultaneously penalizes the propulsion energy and secrecy outage, resulting in a nonlinear risk-sensitive Hamilton-Jacobi-Bellman equation. Simulation results show that there is a significant reduction in secrecy outage probability and key rate variation when atmospheric turbulence exists, but there is only a relatively minor rise in the energy consumption for propulsion, achieving a robustness-efficiency tradeoff for secure aerial quantum communication.