A Compositional Information-Theoretic Framework for Hybrid Quantum–Classical AI Safety

Modern high-assurance systems increasingly integrate quantum components, introducing failure modes that escape classical safety standards: decoherence, entanglement leakage, correlated noise, and quantum fabrication. This paper establishes the foundational theory for hybrid quantum-classical AI safety. It extends the AxoDen framework to quantum systems by enforcing three structural constraints: Thermodynamic (Q-EBDP): bounds entropy injection via CPTP maps, preventing unbounded uncertainty accumulation across hybrid pipelines. 2. Epistemic (Q-EFI): limits model influence via conditional quantum mutual information, preventing algorithmic hallucination where quantum circuits fabricate structure not justified by input. 3. Structural (Q-CFS): ensures independence via basis coprimality, preventing correlated failures across redundant quantum subsystems. The paper derives global compositional bounds proving that local adherence to these constraints guarantees system-wide safety. Key results include the Hybrid Composition Theorem for DAG-structured pipelines, scaling laws for epistemic surplus, and design envelope constraints for certification. This is the foundational theory paper. Operational enforcement, runtime monitoring, and certification protocols are treated in the companion engineering paper (Zenodo DOI 10.5281/zenodo.18282922). Keywords: quantum AI safety, hybrid quantum-classical systems, compositional verification, entropy bounds, CPTP maps, conditional quantum mutual information, basis coprimality, certifiable AI