Curator's Take
This article introduces quantum probabilistic local differential privacy, a relaxed version of quantum local DP that tolerates a small‐probability violation and ties the privacy loss to the acceptance probability of a quantum Neyman‑Pearson test. By establishing composition rules under tensor products, characterizing when depolarising noise meets the new definition, and deriving sample‑complexity bounds via hockey‑stick divergence, it offers a more practical framework for private quantum machine‑learning pipelines than earlier strict DP notions. The work connects privacy guarantees to statistical inference, showing how modest noise can provide meaningful protection while keeping resource demands realistic. Readers should keep in mind that the guarantees are probabilistic, so the failure probability must be carefully calibrated for any deployment.
— Mark Eatherly
Summary
Differential privacy provides a rigorous framework for quantifying privacy leakage in data analysis, while its quantum extensions have become increasingly relevant with the development of quantum computing and quantum machine learning. In this work, we introduce and study quantum probabilistic local differential privacy, a relaxation of quantum local differential privacy in which the privacy constraint is allowed to fail on a spectral violation event with low probability. This quantity can be interpreted as the probability under the quantum superoperation of a quantum privacy-loss violation, and is closely related to the acceptance probability of the quantum Neyman-Pearson test at a small threshold. We investigate the basic structural properties of this privacy notion and clarify its relationship with existing forms of quantum differential privacy. We show the properties of quantum probabilistic local differential privacy under tensor-product composition and unitary post-processing, while it is in general neither convex nor closed under post-processing by arbitrary quantum channels. We further characterize when depolarizing noise satisfies quantum probabilistic local differential privacy under several representative scenarios. Finally, we connect quantum probabilistic privacy constraints with statistical inference by deriving a lower bound on probabilistically privatized contraction coefficients in terms of the hockey-stick divergence. As an application, we obtain sample complexity bounds of probabilistically privated asymmetric and symmetric quantum hypothesis testing. These results provide a systematic foundation for studying probabilistic privacy guarantees in quantum information processing and their operational consequences for private quantum statistical inference.