Quantum–AI Statistical Dangerousness: A Next-Generation Framework for Entangled Risk Modeling

This paper introduces Quantum–AI Statistical Dangerousness (QSD), an advanced probabilistic framework that extends classical Statistical Dangerousness into the domains of quantum information theory and machine learning. The model reconceptualizes systemic risk as a dynamic, non-commutative process, where uncertainties are not only stochastic but also structurally entangled. Within this framework, each system state is represented as a density matrix , enabling the simultaneous treatment of randomness, dependence, and measurement sensitivity. QSD integrates quantum statistical measures—including von Neumann entropy, purity, quantum relative entropy, and a quantum hazard function—to quantify both probabilistic variability and structural instability. By coupling this formalism with artificial intelligence methods, particularly Quantum Generative Adversarial Networks (QGANs) and Transformer-based architectures, the framework learns evolving risk states and forecasts threshold exceedances under complex interdependencies. The learning process aligns classical metrics with quantum representations through tailored loss functions, optimizing prediction of nonlinear and rare-event behavior. The resulting Quantum Dangerousness Index (QDI) unifies exceedance probability, informational entropy, and dynamic hazard into a single, adaptive indicator of systemic dangerousness. Applied across finance and environmental domains, QSD identifies fragile regimes, emergent contagion patterns, and hidden couplings that classical risk models overlook. The framework thus provides a mathematically consistent and computationally intelligent bridge between classical risk analytics and quantum-enhanced forecasting.