Quantum Advantage for Two-Party Differential Privacy

2026-10-01

AI Summary

This study addresses the high-error bottleneck of classical two-party differential privacy protocols under information-theoretic security. We construct quantum communication protocols that leverage non-orthogonal message protection mechanisms to estimate Hamming distance under pure and approximate quantum differential privacy. Through protected coherent round-trip transmission, the isometric Gram rigidity principle, and hockey-stick divergence analysis, we demonstrate for the first time that quantum communication achieves O(1) error under information-theoretic security, matching the precision of classically computationally secure protocols while establishing message retention as a privacy resource. Our approach attains constant expected error with O(n) communication complexity, rigorously separating the security boundaries across distinct privacy models and significantly outperforming classical methods.

Abstract

We introduce information-theoretically private quantum protocols for two-party Hamming distance when both parties must output the same estimate. Classically, for input length $n$, information-theoretic protocols require $Ω(\sqrt{n})$ error under pure differential privacy and $Ω(\sqrt{n}/\log n)$ error under strong approximate differential privacy, whereas computational security permits $O(1)$ error. In Klauck's honest, nonpreemptive, message-preserving model, we give an $O(n)$-communication quantum protocol with pure $\varepsilon$ quantum differential privacy (QDP) and expected error at most $\frac{2}{\sinh \varepsilon}+γ$, for every $γ>0$. For approximate $(\varepsilon, δ)$ QDP, an exact hockey-stick divergence calculation yields strictly smaller error, while preserving the $O(1)$-versus-$Ω(\sqrt{n}/\log n)$ separation for $δ=o(1/n)$. Thus, quantum communication achieves $O(1)$ information-theoretic error, matching the accuracy available classically only under computational assumptions. The main construction uses a guarded coherent round trip and an equal-Gram rigidity principle that prevents an honest player from retaining input-dependent complementary information. We separate this model from weaker prescribed-channel privacy, which already admits an exact classical realization, and from fully retention-robust security, against which measurement-and-abort attacks remain possible. Therefore, we identify preservation of non-orthogonal quantum messages as a resource for privacy.

Problem

• Two-Party Differential Privacy
• Quantum Advantage
• Hamming Distance
• Information-Theoretic Security
• Quantum Communication

Innovation

• Quantum Differential Privacy
• Two-Party Hamming Distance
• Information-Theoretic Security
• Equal-Gram Rigidity
• Hockey-Stick Divergence