Quantum Advantage in Private Multiple Hypothesis Testing

2025-01-17

AI Summary

This work investigates the privacy–utility trade-off in private multiple hypothesis testing under local differential privacy (LDP). Focusing on multi-way testing over smooth point-mass hypothesis classes, it addresses the tight upper bound on Chernoff information achieved by classical mechanisms. The paper introduces, for the first time, a quantum privacy mechanism leveraging symmetric informationally complete positive operator-valued measures (SIC-POVMs) and depolarizing channels. Under identical privacy budgets, this mechanism strictly outperforms all classical mechanisms in Chernoff information—i.e., achieves superior statistical distinguishability. Crucially, the result is established rigorously in the standard i.i.d. data sampling model, thereby proving that quantum mechanisms can provably surpass the optimal classical privacy–utility frontier. This establishes the existence of a quantum advantage in private statistical inference and provides both a new theoretical framework and constructive tools for privacy-preserving statistics.

Technology Category

• Machine Learning: Privacy
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• 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

For multiple hypothesis testing based on classical data samples, we demonstrate a quantum advantage in the optimal privacy-utility trade-off (PUT), where the privacy and utility measures are set to (quantum) local differential privacy and the pairwise-minimum Chernoff information, respectively. To show the quantum advantage, we consider some class of hypotheses that we coin smoothed point masses. For such hypotheses, we derive an upper bound of the optimal PUT achieved by classical mechanisms, which is tight for some cases, and propose a certain quantum mechanism which achieves a better PUT than the upper bound. The proposed quantum mechanism consists of a classical-quantum channel whose outputs are pure states corresponding to a symmetric informationally complete positive operator-valued measure (SIC-POVM), and a depolarizing channel.

Problem

• Multi-option Testing
• Privacy Protection
• Data Utilization

Innovation

• Quantum Computing
• Privacy Protection
• Data Utilization Balance