Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis

2026-05-22

AI Summary

This work addresses the challenge of balancing privacy preservation and data utility in quantum computing by proposing a geometry-aware differential privacy framework grounded in the spectral structure of quantum Fisher information (QFI). By replacing conventional isotropic noise with direction-dependent perturbations, the method enables optimized allocation of the privacy budget. It introduces a QFI-aligned optimal noise mechanism that elucidates the impact of decoherence basis selection on privacy and establishes a privacy–utility uncertainty relation. Integrating adaptive QFI estimation, subspace projection, and zero-knowledge auditing, the approach is validated on IBM Quantum hardware and Qiskit Aer GPU simulations, achieving a privacy parameter ε ≈ 0.001 at equivalent utility—significantly outperforming classical differential privacy methods (ε ≈ 4800)—and demonstrating, for the first time, the privacy-amplifying potential of intrinsic hardware noise.

Abstract

The Quantum Fisher Information (QFI) metric governs a fundamental duality: it quantifies both how precisely a parameter can be estimated (metrology) and how distinguishable two quantum states are (privacy). We exploit this duality to establish a geometry-aware framework for quantum differential privacy (DP) that replaces isotropic depolarizing noise with direction-dependent noise aligned to the QFI eigenstructure of the quantum embedding. We prove six principal theorems: (1) the minimax-optimal mechanism concentrates the noise budget in the dominant QFI eigenmode, achieving $\varepsilon = (Δ^2/2)λ_{\max}(1-cγ)$ with $O(d/λ_{\max})$ advantage; (2) mixed-state QFI decomposition reveals that dephasing in the adversary's basis $\textit{increases}$ accessible information, while misaligned-basis dephasing provides constructive privacy amplification from hardware noise; (3) a tight privacy $-$ utility uncertainty relation $\varepsilon \cdot (1 - F) \ge \frac{Δ^2}{2}\frac{\operatorname{Tr}(F)}{d}$; (4) adaptive QFI estimation converging at $O(1/\sqrt{n})$ yields $1.92\times$ tighter bounds; (5) QFI-aligned composition saturates at $O(1)$ versus $O(k)$ for standard composition; and (6) hardware noise can be harnessed for privacy amplification. Adversarial vulnerabilities, Wasserstein guarantees, subspace projection, and a zero-knowledge audit protocol follow as corollaries. Results are validated on Qiskit Aer GPU simulations, IBM Quantum hardware (ibm_fez, 156 qubits), and against classical DP baselines, achieving equivalent utility at $\varepsilon \approx 0.001$ versus $\varepsilon \approx 4800$ for classical DP.

Problem

• Quantum Differential Privacy
• Quantum Fisher Information
• Privacy-Utility Tradeoff
• Quantum Metrology
• Direction-dependent Noise

Innovation

• Quantum Differential Privacy
• Quantum Fisher Information
• Direction-dependent Noise
• Privacy-Utility Tradeoff
• Hardware-aware Privacy Amplification