Adversarial Limits of Quantum Certification: When Eve Defeats Detection

Abstract: Security of quantum key distribution (QKD) relies on certifying that observed correlations arise from genuine quantum entanglement rather than eavesdropper manipulation. Theoretical security proofs assume idealized conditions, practical certification must contend with adaptive adversaries who optimize their attack strategies against detection systems. Established fundamental adversarial limits for quantum certification using Eve GAN, a generative adversarial network trained to produce classical correlations indistinguishable from quantum. Our central finding: when Eve interpolates her classical correlations with quantum data at mixing parameter, all tested detection methods achieve ROC AUC = 0.50, equivalent to random guessing. This means an eavesdropper needs only 5% classical admixture to completely evade detection. Critically, we discover that same distribution calibration a common practice in prior certification studies inflates detection performance by 44 percentage points compared to proper cross distribution evaluation, revealing a systematic flaw that may have led to overestimated security claims. Analysis of Popescu Rohrlich (PR Box) regime identifies a sharp phase transition at CHSH S = 2.05: below this value, no statistical method distinguishes classical from quantum correlations; above it, detection probability increases monotonically. Hardware validation on IBM Quantum demonstrates that Eve-GAN achieves CHSH = 2.736, remarkably exceeding real quantum hardware performance (CHSH = 2.691), illustrating that classical adversaries can outperform noisy quantum systems on standard certification metrics. These results have immediate implications for QKD security: adversaries maintaining 95% quantum fidelity evade all tested detection methods. We provide corrected methodology using cross-distribution calibration and recommend mandatory adversarial testing for quantum security claims.