Privacy Implies Stability: Information-Theoretic Generalization Bounds for Quantum Learning

arXiv:2602.01177v3 Announce Type: replace-cross Abstract: We develop an information-theoretic framework connecting stability, privacy, and generalization for quantum learning algorithms. Learning procedures are modeled as quantum instruments with classical-quantum outputs, and losses are represented by observables. We prove that under a classical-quantum sub-Gaussian condition, an information-theoretic stability measure controls the expected generalization error. Furthermore, we establish a high-probability generalization bound using quantum R\'enyi divergences to manage higher-order dependenc