Abstract:We optimize the trade-off between privacy and utility in the high-privacy regime. We adopt local differential privacy (LDP) and its quantum extension, quantum local differential privacy (QLDP), for privacy protection, and investigate utility functions including the Holevo information (which reduces to the mutual information in the classical case) and the error exponents in symmetric and asymmetric hypothesis testing. Under the LDP and QLDP constraints, these utility functions have classical and quantum optimal values, which we denote simply by $C$ and $Q$, respectively, in this abstract. In this paper, we provide optimal LDP and QLDP mechanisms achieving the classical and quantum optimal values in the high-privacy regime, and prove that the asymptotic ratio $Q/C$ in this regime takes the same value regardless of the utility function. Our results reveal quantum advantages (specifically, $Q/C\ge3/2$) for the above utility functions when the private data take at least three possible values. In addition, conditional on a mathematical conjecture concerning equi-isoclinic tight fusion frames (EITFFs), our QLDP mechanisms also exhibit quantum advantages in a moderate-privacy regime.
From: Yuuya Yoshida [view email]
[v1]
Tue, 26 May 2026 16:57:22 UTC (74 KB)
[v2]
Mon, 8 Jun 2026 12:02:11 UTC (78 KB)
[v3]
Thu, 3 Sep 2026 19:38:31 UTC (119 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。