Equivalence of Privacy and Stability with Generalization Guarantees in Quantum Learning
This work addresses the challenge of ensuring privacy and generalization in quantum machine learning, which is incremental as it extends classical differential privacy concepts to the quantum domain with theoretical guarantees.
The paper tackles the problem of analyzing generalization performance in differentially private quantum learning algorithms by establishing a unified information-theoretic framework that connects privacy, stability, and generalization, proving that the expected generalization error is bounded by the square root of a privacy-induced stability term.
We present a unified information-theoretic framework to analyze the generalization performance of differentially private (DP) quantum learning algorithms. By leveraging the connection between privacy and algorithmic stability, we establish that $(\varepsilon, δ)$-Quantum Differential Privacy (QDP) imposes a strong constraint on the mutual information between the training data and the algorithm's output. We derive a rigorous, mechanism-agnostic upper bound on this mutual information for learning algorithms satisfying a 1-neighbor privacy constraint. Furthermore, we connect this stability guarantee to generalization, proving that the expected generalization error of any $(\varepsilon, δ)$-QDP learning algorithm is bounded by the square root of the privacy-induced stability term. Finally, we extend our framework to the setting of an untrusted Data Processor, introducing the concept of Information-Theoretic Admissibility (ITA) to characterize the fundamental limits of privacy in scenarios where the learning map itself must remain oblivious to the specific dataset instance.