发表机构
University of Illinois at Urbana-Champaign; Joint Center for Quantum Information and Computer Science, NIST/University of Maryland; Joint Quantum Institute, NIST/University of Maryland（伊利诺伊大学厄巴纳-香槟分校; 量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学; 量子研究所，美国国家标准与技术研究院/马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子协议实现两方汉明距离的信息论隐私，达到O(1)误差，超越经典信息论下界，利用相干往返和等格刚性原理，揭示非正交量子消息作为隐私资源。
AI 中文摘要
我们引入了信息论上私密的量子协议，用于两方汉明距离计算，且双方必须输出相同的估计值。在经典情况下，对于输入长度 $n$，信息论协议在纯差分隐私下需要 $\Omega(\sqrt{n})$ 的误差，在强近似差分隐私下需要 $\Omega(\sqrt{n}/\log n)$ 的误差，而计算安全性允许 $O(1)$ 的误差。在Klauck的诚实、非抢占、消息保留模型中，我们给出了一个 $O(n)$ 通信复杂度的量子协议，具有纯 $\varepsilon$ 量子差分隐私（QDP），且期望误差至多为 $\frac{2}{\sinh \varepsilon}+\gamma$，对于任意 $\gamma>0$。对于近似 $(\varepsilon, \delta)$ QDP，精确的hockey-stick散度计算产生严格更小的误差，同时保持 $O(1)$ 与 $\Omega(\sqrt{n}/\log n)$ 的分离，当 $\delta=o(1/n)$ 时。因此，量子通信实现了 $O(1)$ 的信息论误差，匹配了经典情况下仅在计算假设下才可用的精度。主要构造使用了受保护的相干往返行程和一个等格刚性原理，该原理防止诚实方保留输入相关的互补信息。我们将此模型与较弱的指定信道隐私区分开来，后者已经允许精确的经典实现，并与完全保留鲁棒安全性区分开来，针对后者，测量和弃权（不执行）攻击仍然可能发生。因此，我们将保留非正交量子消息识别为一种隐私资源。
英文摘要
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.
Comments15 + 7 pages, 2 figures. Also on ePrint
