Quantum key distribution (QKD) security fundamentally relies on the ability to distinguish genuine quantum correlations from classical eavesdropper simulations, yet existing certification methods lack rigorous statistical guarantees under finite-sample conditions and adversarial scenarios. We introduce TARA (Test by Adaptive Ranks), a novel framework combining conformal prediction with sequential martingale testing for quantum anomaly detection that provides distribution-free validity guarantees. TARA offers two complementary approaches. TARA k, based on Kolmogorov Smirnov calibration against local hidden variable (LHV) null distributions, achieving ROC AUC = 0.96 for quantum-classical discrimination. And TARA-m, employing betting martingales for streaming detection with anytime valid type I error control that enables real time monitoring of quantum channels. We establish theoretical guarantees proving that under (context conditional) exchangeability, conformal p-values remain uniformly distributed even for strongly contextual quantum data, confirming that quantum contextuality does not break conformal prediction validity a result with implications beyond quantum certification to any application of distribution-free methods to nonclassical data. Extensive validation on both IBM Torino (superconducting, CHSH = 2.725) and IonQ Forte Enterprise (trapped ion, CHSH = 2.716) quantum processors demonstrates cross-platform robustness, achieving 36% security margins above the classical CHSH bound of 2. Critically, our framework reveals a methodological concern affecting quantum certification more broadly: same-distribution calibration can inflate detection performance by up to 44 percentage points compared to proper cross-distribution calibration, suggesting that prior quantum certification studies using standard train test splits may have systematically overestimated adversarial robustness.
Quantum key distribution (QKD) security fundamentally relies on the ability to distinguish genuine quantum correlations from classical eavesdropper simulations, yet existing certification methods lack rigorous statistical guarantees under finite-sample conditions and adversarial scenarios. We introduce TARA (Test by Adaptive Ranks), a novel framework combining conformal prediction with sequential martingale testing for quantum anomaly detection that provides distribution-free validity guarantees. TARA offers two complementary approaches. TARA k, based on Kolmogorov Smirnov calibration against local hidden variable (LHV) null distributions, achieving ROC AUC = 0.96 for quantum-classical discrimination. And TARA-m, employing betting martingales for streaming detection with anytime valid type I error control that enables real time monitoring of quantum channels. We establish theoretical guarantees proving that under (context conditional) exchangeability, conformal p-values remain uniformly distributed even for strongly contextual quantum data, confirming that quantum contextuality does not break conformal prediction validity a result with implications beyond quantum certification to any application of distribution-free methods to nonclassical data. Extensive validation on both IBM Torino (superconducting, CHSH = 2.725) and IonQ Forte Enterprise (trapped ion, CHSH = 2.716) quantum processors demonstrates cross-platform robustness, achieving 36% security margins above the classical CHSH bound of 2. Critically, our framework reveals a methodological concern affecting quantum certification more broadly: same-distribution calibration can inflate detection performance by up to 44 percentage points compared to proper cross-distribution calibration, suggesting that prior quantum certification studies using standard train test splits may have systematically overestimated adversarial robustness.
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.
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.
Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.
We develop a practical framework for semi-device-independent (SDI) certification under operational deviations from the ideal protocol model. Apparent violations of classical benchmarks need not signal genuinely non-classical behaviour; they can arise from misalignment between (i) the scoring rule, (ii) the finite-sample statistical bound applied to that score, and (iii) the operational model realised in the experiment, including bias, memory, drift, and selection effects.
We formalise a protocol-agnostic alignment principle based on a martingale-safe lower confidence bound and an operationally consistent effective classical ceiling. This yields a quantitative diagnostic, the \emph{robustness gap} Δrob=Slow−SC,eff, which separates statistical fluctuations from structural modelling errors. Statistical deviations vanish asymptotically, whereas model misalignment can produce persistent false certification unless the benchmark is corrected.
Using the 2→1 random access code as a minimal SDI testbed, we show that postselection can inflate conditional scores, whereas unconditional scoring restores the correct operational meaning of the witness. We further show that adaptive learning-based classical agents do not enlarge the admissible classical set; rather, they recover the effective classical ceiling implied by the operational model.
The resulting framework provides a systematic diagnostic for certification in realistic quantum communication and measurement settings with embedded classical control, adaptive processing, and nonideal data acquisition.
Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need for reliable and trustworthy predictions. Recent work has introduced quantum conformal prediction, a framework that produces prediction sets that are guaranteed to contain the true outcome with a user-specified probability. In this work, we formalise how the time-varying noise inherent in quantum processors can undermine conformal guarantees, even when calibration and test data are exchangeable. To address this challenge, we draw on Adaptive Conformal Inference, a method which maintains validity over time via repeated recalibration. We introduce Adaptive Quantum Conformal Prediction (AQCP), an algorithm which provides asymptotic average coverage guarantees under arbitrary hardware noise conditions. Empirical studies on an IBM quantum processor demonstrate that AQCP achieves the target coverage level and exhibits greater stability than quantum conformal prediction.
Abstract Operator learning enables fast surrogate modelling of high-dimensional dynam-ical systems, but existing approaches face two fundamental limitations: the quadratic cost of dense neural layers and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum Deep Operator Network (DeepONet) Ensembles, a framework that addresses both challenges simultaneously. Using Quantum Orthogonal Neural Networks (QOrthoNNs), we characterize the resource regime in which their established˜︁established˜︁ O(n) hidden-layer running-time scaling improves on the O(n 2) cost of a classical dense layer. To quantify uncertainty, we combine ensemble predictions with split conformal calibration. For a new input–output function pair jointly exchangeable with the calibration pairs, we prove a finite-sample, distribution-free lower bound on the expected fraction of covered query locations. As a secondary proof-of-concept, we explore hybrid classical–quantum architectures and superposed execution to manage ensemble runtime and hardware requirements. Experiments on synthetic operator benchmarks and real-world power-system dynamics show accurate predictions under ideal simulation and empirical coverage near the target under both ideal conditions and selected compact-circuit simulations with depolarizing 1 or device-calibrated composite noise. Together, these results connect resource-aware scalability analysis with finite-sample uncertainty guarantees for quantum operator learning.