Privacy-Utility Tradeoffs in Quantum Information Processing

2026-02-11

AI Summary

This work investigates the optimal privacy–utility trade-off for learning tasks under (ε,δ)-quantum local differential privacy. In the general setting, the depolarizing mechanism is proven optimal through analyses based on fidelity and trace distance. For the specific task of estimating expectation values of observables, the study introduces, for the first time, a private classical shadow framework and leverages a lower bound from private quantum hypothesis testing to establish a sample complexity of Θ((εβ)⁻²). Building on this fundamental limit, the authors design an efficient private mechanism that matches the lower bound, thereby achieving task-specific optimality in the privacy–utility trade-off.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

When sensitive information is encoded in data, it is important to ensure the privacy of information when attempting to learn useful information from the data. There is a natural tradeoff whereby increasing privacy requirements may decrease the utility of a learning protocol. In the quantum setting of differential privacy, such tradeoffs between privacy and utility have so far remained largely unexplored. In this work, we study optimal privacy-utility tradeoffs for both generic and application-specific utility metrics when privacy is quantified by $(\varepsilon,\delta)$-quantum local differential privacy. In the generic setting, we focus on optimizing fidelity and trace distance between the original state and the privatized state. We show that the depolarizing mechanism achieves the optimal utility for given privacy requirements. We then study the specific application of learning the expectation of an observable with respect to an input state when only given access to privatized states. We derive a lower bound on the number of samples of privatized data required to achieve a fixed accuracy guarantee with high probability. To prove this result, we employ existing lower bounds on private quantum hypothesis testing, thus showcasing the first operational use of them. We also devise private mechanisms that achieve optimal sample complexity with respect to the privacy parameters and accuracy parameters, demonstrating that utility can be significantly improved for specific tasks in contrast to the generic setting. In addition, we show that the number of samples required to privately learn observable expectation values scales as $\Theta((\varepsilon \beta)^{-2})$, where $\varepsilon \in (0,1)$ is the privacy parameter and $\beta$ is the accuracy tolerance. We conclude by initiating the study of private classical shadows, which promise useful applications for private learning tasks.

Problem

• privacy-utility tradeoff
• quantum differential privacy
• quantum local differential privacy
• observable expectation learning
• private quantum information processing

Innovation

• quantum differential privacy
• privacy-utility tradeoff
• depolarizing mechanism
• private quantum learning
• classical shadows