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TARA Test-by-Adaptive-Ranks for Quantum Anomaly Detection with Conformal Prediction Guarantees

Davut Emre Tasar, Ceren Ocal Tasar

TL;DR

The paper introduces TARA, a framework that combines conformal prediction with martingale testing to provide distribution-free guarantees for quantum anomaly detection in device-independent certification. It presents two detectors: TARA-k for batch discrimination against LHV models achieving ROC AUC = 0.96, and TARA-m for streaming monitoring with anytime-valid error control. Theoretical results show conformal prediction remains valid under context-conditional exchangeability despite quantum contextuality, and hardware validation across IBM Torino and IonQ Forte demonstrates cross-platform robustness with ~36% margins above the classical CHSH bound. A notable finding is the calibration leakage problem, where same-distribution calibration inflates performance by up to 44 percentage points, underscoring the importance of cross-distribution evaluation in quantum certification.

Abstract

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.

TARA Test-by-Adaptive-Ranks for Quantum Anomaly Detection with Conformal Prediction Guarantees

TL;DR

The paper introduces TARA, a framework that combines conformal prediction with martingale testing to provide distribution-free guarantees for quantum anomaly detection in device-independent certification. It presents two detectors: TARA-k for batch discrimination against LHV models achieving ROC AUC = 0.96, and TARA-m for streaming monitoring with anytime-valid error control. Theoretical results show conformal prediction remains valid under context-conditional exchangeability despite quantum contextuality, and hardware validation across IBM Torino and IonQ Forte demonstrates cross-platform robustness with ~36% margins above the classical CHSH bound. A notable finding is the calibration leakage problem, where same-distribution calibration inflates performance by up to 44 percentage points, underscoring the importance of cross-distribution evaluation in quantum certification.

Abstract

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.

Paper Structure

This paper contains 15 sections, 3 theorems, 14 equations, 3 figures, 2 tables.

Table of Contents

  1. Keywords:
  2. Introduction
  3. Background
  4. Conformal Prediction
  5. The CHSH Bell Scenario
  6. The TARA Framework
  7. TARA-$k$: Batch Detection
  8. TARA-$m$: Streaming Detection
  9. Theoretical Guarantees
  10. Experimental Results
  11. Hardware Validation
  12. The 44-Point Leakage Problem
  13. Discussion
  14. Related Work on Quantum Certification
  15. Conclusion

Key Result

Theorem 1

Under exchangeability of $\mathcal{D}_{\mathrm{cal}} \cup \{(X_{n+1}, Y_{n+1})\}$, the conformal $p$-values satisfy: for any $\alpha \in (0, 1)$, any sample size $n$, and any distribution $P$.

Figures (3)

  • Figure 1: ROC curve for TARA-$k$ quantum-classical discrimination. The detector achieves AUC = 0.96 against a comprehensive LHV null manifold including detection, memory, and communication loophole models.
  • Figure 2: TARA-$m$ martingale wealth trajectories. Under the LHV null (gray), wealth does not grow. Under the quantum alternative (blue), wealth grows and crosses the detection threshold.
  • Figure 3: Same-distribution calibration inflates apparent detection performance by 44 percentage points compared to proper cross-distribution calibration.

Theorems & Definitions (10)

  • Definition 1: Split Conformal Prediction
  • Theorem 1: Coverage Guarantee Vovk2005
  • Definition 2: LHV Null Manifold
  • Definition 3: Feature Vector
  • Definition 4: Betting Martingale
  • Proposition 2: Martingale Validity
  • proof
  • Theorem 3: CP Robustness to Contextuality
  • proof
  • Remark 1