A Risk-Aware Framework for Covert Quantum Communication under Stochastic Channel Uncertainty

Covert quantum communication (CQC) seeks to hide not only message content but also the existence of communication. Existing CQC models usually assume deterministic or worst-case channel conditions, which are difficult to justify in realistic free-space optical and quantum links affected by turbulence, fluctuating background radiance, and stochastic detector noise. We propose a stochastic risk-aware optimization framework for CQC under uncertain physical-layer conditions. By modeling transmissivity and background noise as random variables, we express covertness and reliability guarantees through chance constraints with explicit outage budgets $ε_{\text{cov}}$ and $ε_{\text{rel}}$. This recasts CQC design as a risk-calibrated resource-allocation problem balancing throughput, covertness, reliability, and communication privacy. We derive quantile-based reformulations of the outage constraints, characterize feasible operating regions under stochastic uncertainty, and introduce a complementary risk-adjusted utility formulation to expose throughput-risk trade-offs. The analysis reveals that modest relaxations in acceptable covertness-outage risk can yield large throughput gains, while aggressive optimization may break covertness outside sparse-transmission regimes. Monte Carlo results under log-normal fading and stochastic thermal noise show that the framework expands feasible operating regions, improves covert throughput by more than an order of magnitude, and identifies degradation boundaries beyond which covert operation becomes unreliable. These results move CQC closer to realistic secure quantum networking for free-space, satellite, and low-probability-of-detection applications.