Equivalence of Privacy and Stability with Generalization Guarantees in Quantum Learning

• URL: http://arxiv.org/abs/2602.01177v2
• Date: Thu, 05 Feb 2026 10:06:53 GMT
• Title: Equivalence of Privacy and Stability with Generalization Guarantees in Quantum Learning
• Authors: Ayanava Dasgupta, Naqueeb Ahmad Warsi, Masahito Hayashi,
• Abstract summary: We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms.<n>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.<n>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.
• Score: 42.694152897125726
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $(\varepsilon, δ)$-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.

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