Equivalence of Privacy and Stability with Generalization Guarantees in Quantum Learning

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.

💡 Research Summary

This paper develops a unified information‑theoretic framework that connects algorithmic stability, differential privacy, and generalization performance for quantum learning algorithms. The authors model a quantum learning protocol as an interaction among three parties—Respondents who contribute data, a Data Processor that runs a quantum learning algorithm, and an Investigator who receives the hypothesis. They first define stability in the quantum setting via the mutual information I