Conformal Prediction for Quantum Entanglement: Robustness and Detection

Certification of quantum entanglement under realistic device imperfections is central to quantum communication, cryptography, and quantum networks. Despite the nonclassical nature of entanglement and contextuality, we empirically verify that standard Conformal Prediction(CP)retainsitscoverageguaranteesintheCHSHscenario, astheoreticallyexpected under (context-conditional) exchangeability. We introduce an LHV-Calibrated Anomaly Detection framework achieving an ROC AUC ≈0.96 (Scenario A) and AUC ≈0.83 using only CP-derived features (Scenario B). Validation on IBM quantum hardware (Shw ≈2.53) confirms these results under Noisy Intermediate-Scale Quantum (NISQ) conditions, relative to an explicit LHV null manifold. Finally, we prove a no-go theorem for product-threshold Conformal Entanglement Witnesses (CEW), explaining their limited power. Our results suggest that, at least in the CHSH setting considered here, CP is best viewed as a robust statistical wrapper around quantum devices, rather than a fragile entanglement witness. To facilitate reproducibility, all code, data, and experiment configurations are available at https://github.com/detasar/QCE.