Quantum Blackwell's Ordering and Differential Privacy

2025-11-03

AI Summary

This work establishes the first unified framework for quantum differential privacy (QDP) grounded in quantum hypothesis testing and the Blackwell order, rigorously characterizing $(varepsilon,delta)$-QDP and identifying information-optimal quantum state pairs under privacy constraints. Methodologically, it introduces the Blackwell order and hockey-stick divergence to QDP—enabling a nontrivial extension of classical differential privacy to the $delta > 0$ quantum regime—and derives near-optimal contraction bounds for QDP channels by integrating quantum Fisher information with hypothesis-testing divergences. Key contributions are: (1) tight theoretical bounds on the privacy–accuracy trade-off; (2) the first exact characterization of private quantum parameter estimation performance; and (3) empirical validation of the framework’s efficacy in stability analysis of quantum learning algorithms. The work bridges quantum information theory and privacy-preserving computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We develop a framework for quantum differential privacy (QDP) based on quantum hypothesis testing and Blackwell's ordering. This approach characterizes $(eps,δ)$-QDP via hypothesis testing divergences and identifies the most informative quantum state pairs under privacy constraints. We apply this to analyze the stability of quantum learning algorithms, generalizing classical results to the case $δ>0$. Additionally, we study privatized quantum parameter estimation, deriving tight bounds on the quantum Fisher information under QDP. Finally, we establish near-optimal contraction bounds for differentially private quantum channels with respect to the hockey-stick divergence.

Problem

• Developing quantum differential privacy via hypothesis testing
• Analyzing stability of quantum learning algorithms with privacy
• Establishing tight bounds for private quantum parameter estimation

Innovation

• Framework uses quantum hypothesis testing for privacy
• Applies privacy constraints to quantum learning algorithms
• Derives bounds on quantum Fisher information under privacy