Abstract:We consider a private hypothesis testing scenario, including both symmetric and asymmetric testing, based on classical data samples. The utility is measured by the error exponents, namely the Chernoff information and the relative entropy, while privacy is measured in terms of classical or quantum local differential privacy. In this scenario, we show a quantum advantage with respect to the optimal privacy-utility trade-off (PUT) in certain cases. Specifically, we focus on distributions referred to as smoothed point mass distributions, along with the uniform distribution, as hypotheses. We then derive upper bounds on the optimal PUTs achievable by classical privacy mechanisms, which are tight in specific instances. To show the quantum advantage, we propose a particular quantum privacy mechanism that achieves better PUTs than these upper bounds in both symmetric and asymmetric testing, specifically under stringent privacy constraints and small discrete data alphabet sizes ranging from 3 to 9. The proposed mechanism consists of a classical-quantum channel that prepares symmetric informationally complete (SIC) states, followed by a depolarizing channel.
From: Seung-Hyun Nam [view email]
[v1]
Fri, 17 Jan 2025 12:23:43 UTC (59 KB)
[v2]
Thu, 13 Feb 2025 03:46:30 UTC (65 KB)
[v3]
Fri, 29 Aug 2025 08:10:25 UTC (1,213 KB)
[v4]
Tue, 30 Jun 2026 09:54:25 UTC (1,106 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。