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

Source: arXiv - 2512.04016v1

Overview

The paper introduces TARA (Test‑by‑Adaptive‑Ranks), a new statistical framework that blends conformal prediction with sequential martingale testing to detect anomalies in quantum communication channels. By delivering distribution‑free guarantees even with limited data, TARA promises more reliable certification of quantum key distribution (QKD) systems and other quantum‑information protocols.

Key Contributions

• TARA‑k: A Kolmogorov‑Smirnov (KS)‑based conformal test that distinguishes genuine quantum correlations from classical (local‑hidden‑variable) simulations, achieving an ROC‑AUC of 0.96.
• TARA‑m: A streaming‑compatible version that uses betting martingales to provide any‑time type‑I error control, enabling real‑time monitoring of quantum channels.
• Theoretical guarantee: Proves that conformal p‑values stay uniformly distributed under (context‑conditional) exchangeability, even for strongly contextual quantum data.
• Cross‑platform validation: Demonstrates robustness on IBM Torino (superconducting) and IonQ Forte (trapped‑ion) processors, each exceeding the classical CHSH bound by ~36 %.
• Methodological insight: Shows that naïve same‑distribution calibration can overstate detection performance by up to 44 %, highlighting a hidden bias in many prior quantum‑certification studies.

Methodology

1. Data Generation – The authors collect measurement outcomes from Bell‑test experiments (CHSH games) on two different quantum hardware platforms. Each run yields a binary outcome vector that can be modeled as either:

   • Quantum (violating the CHSH inequality) or
   • Classical (compatible with a local hidden‑variable model).

2. Conformal Prediction Layer – For a batch of observations, a non‑conformity score is computed (e.g., distance from the empirical distribution under the LHV null). The scores are then ranked adaptively, producing conformal p‑values that are provably uniform under the null hypothesis, regardless of the underlying distribution.

3. TARA‑k (Batch Test) – The conformal p‑values are fed into a Kolmogorov‑Smirnov test that compares the empirical distribution against the uniform reference. A low KS statistic signals an anomaly (i.e., genuine quantum behavior).

4. TARA‑m (Sequential Test) – Instead of waiting for a full batch, each new observation updates a betting martingale that “bets” on the null being true. The martingale’s growth rate serves as an anytime test statistic; crossing a pre‑set threshold triggers an anomaly alert while preserving a strict type‑I error bound.

5. Cross‑Distribution Calibration – To avoid the over‑optimistic bias of same‑distribution splits, the authors deliberately calibrate the conformal scores on data drawn from a different hardware platform, mimicking a realistic adversarial scenario.

Results & Findings

Interpretation: TARA reliably flags quantum‑generated data even when the adversary tailors classical simulations to mimic quantum statistics. The streaming version can raise alerts after just a few dozen shots, making it suitable for live QKD monitoring.

Practical Implications

• Real‑time QKD security – Operators can embed TARA‑m into the key‑generation pipeline to continuously verify that the channel remains genuinely quantum, aborting sessions the moment an anomaly is detected.
• Hardware‑agnostic certification – Because the guarantees are distribution‑free, the same test can be deployed across superconducting, trapped‑ion, photonic, or emerging quantum platforms without re‑tuning statistical models.
• Tooling for developers – The underlying conformal‑prediction and martingale code are lightweight (Python‑compatible) and can be wrapped as a library or micro‑service, enabling easy integration with existing quantum SDKs (Qiskit, Cirq, IonQ SDK).
• Broader anomaly‑detection – The framework’s independence from data distribution makes it attractive for other non‑classical streams (e.g., quantum sensor networks, variational algorithm outputs) where traditional statistical tests fail.
• Auditability – Uniform p‑values provide a clear, interpretable metric that can be logged and audited, satisfying compliance requirements for high‑assurance quantum communications.

Limitations & Future Work

• Exchangeability assumption – The theoretical guarantees hinge on (context‑conditional) exchangeability of the data; strong temporal correlations or drifts could weaken validity.
• Scalability to high‑dimensional observables – Current experiments focus on binary Bell‑test outcomes; extending TARA to multi‑outcome or continuous‑variable measurements may require more sophisticated non‑conformity scores.
• Adversarial model scope – The paper evaluates classical LHV attacks; future work should explore more sophisticated quantum‑classical hybrid attacks and side‑channel leakage.
• Hardware integration – While the authors provide a proof‑of‑concept implementation, production‑grade deployment will need robust handling of latency, fault tolerance, and secure key management.

Bottom line: TARA offers a mathematically rigorous, developer‑friendly toolbox for quantum anomaly detection, paving the way for more trustworthy quantum communication services and opening new avenues for distribution‑free testing in other quantum‑technology domains.

Authors

• Davut Emre Tasar
• Ceren Ocal Tasar

Paper Information

• arXiv ID: 2512.04016v1
• Categories: quant-ph, cs.AI
• Published: December 3, 2025
• PDF: Download PDF