Equivalence of Privacy and Stability with Generalization Guarantees in Quantum Learning

2026-02-01

AI Summary

This work investigates the theoretical interplay among differential privacy, algorithmic stability, and generalization in quantum learning. By constructing a unified information-theoretic framework, it establishes—for the first time—a quantitative relationship between quantum differential privacy (QDP) and generalization error, yielding a mechanism-independent upper bound on mutual information. The study further introduces the notion of information-theoretic admissibility (ITA) to characterize fundamental privacy limits under untrusted data processors. A key contribution is the proof that the expected generalization error of any $(\varepsilon, \delta)$-QDP quantum learning algorithm is controlled by the square root of a privacy-induced stability term, thereby providing a rigorous generalization bound and laying a theoretical foundation for understanding the privacy-generalization trade-off in quantum learning systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms. We establish a bound on the expected generalization error in terms of quantum mutual information and derive a probabilistic upper bound that generalizes the classical result by Esposito et al. (2021). Complementing these findings, we provide a lower bound on the expected true loss relative to the expected empirical loss. Additionally, we demonstrate that $(\varepsilon, \delta)$-quantum differentially private learning algorithms are stable, thereby ensuring strong generalization guarantees. Finally, we extend our analysis to dishonest learning algorithms, introducing Information-Theoretic Admissibility (ITA) to characterize the fundamental limits of privacy when the learning algorithm is oblivious to specific dataset instances.

Problem

• Quantum Differential Privacy
• Generalization
• Algorithmic Stability
• Information-Theoretic Admissibility
• Mutual Information

Innovation

• Quantum Differential Privacy
• Algorithmic Stability
• Generalization Error
• Mutual Information
• Information-Theoretic Admissibility