论文简报
quant-ph 2605.27278v1 必读

Optimal quantum locally differentially private mechanisms in the high-privacy regime

Yuuya Yoshida

发布日期：2026-05-26 16:57 相关性：1.0000 价值：0.8200 分类：quant-ph cs.IT
arXiv 摘要 PDF 原文 网页正文

摘要

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. These utility functions have classical and quantum optimal values, which are denoted by $C$ and $Q$, respectively, in this abstract for simplicity. 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 (more precisely, $Q/C\ge3/2$) for the above utility functions when the protected private data are $n$-ary with $n\ge3$.

相关性判断

high
相关方向
information_theory privacy quantum_information hypothesis_testing
判断依据

The paper is directly about local differential privacy and quantum local differential privacy, with utility measures tied to mutual information/Holevo information and hypothesis testing error exponents, which are adjacent to information theory and communications. It is relevant for later review.

价值判断

Directly relevant to information theory, privacy, quantum information, and hypothesis testing, with high-confidence prior relevance and a clear need_full_review signal. Structure analysis identifies concrete optimality claims for LDP/QLDP mechanisms, unified quantum/classical asymptotic ratios across several utilities, and claimed quantum advantage for n-ary data. Technical evidence is substantial: high-privacy asymptotics, Petz monotone metrics, Frechet-derivative expansions, EITFF-based mechanisms, and Chernoff/error-exponent analysis.

核心问题与主要方法

核心问题

Optimize privacy-utility trade-offs under classical LDP and quantum LQLDP, and determine whether quantum mechanisms outperform classical ones

场景：Finite n-ary local privacy model in the high-privacy regime ε→0, comparing classical LDP mechanisms with quantum states under QLDP for utility functions such as Holevo information and hypothesis-testing error exponents

主要方法

Reduces the high-privacy regime to second-order asymptotics around indistinguishable mechanisms, with the quantum utility expansion expressed through a normalized Petz monotone metric. Uses symmetry and sublinearity of the classical utility to obtain classical optimal values and to justify binary mechanisms as high-privacy optimal LDP mechanisms. Constructs QLDP mechanisms from equi-isoclinic tight fusion frames; the resulting isoclinic mechanisms are shown to satisfy QLDP and achieve the quantum optimum asymptotically. Applies Chernoff-information and relative-entropy expansions to symmetric and asymmetric hypothesis-testing error exponents.

关键贡献与后续阅读

关键贡献

Characterizes optimal LDP and QLDP mechanisms in the high-privacy regime for a broad class of utilities whose classical form is a symmetric sublinear sum and whose quantum extension has a specified second-order Taylor term. Shows that the asymptotic quantum/classical optimal-value ratio is utility-independent across the studied class, covering Holevo information and hypothesis-testing error exponents. Establishes quantum advantage for n-ary private data with n>=3 for Holevo information and symmetric/asymmetric hypothesis-testing utilities, extending concrete information-processing advantage claims to n>=10. Improves or resolves optimality of prior Nam et al. results in stated parameter ranges, including strict improvements for some n in {5,...,9} and agreement in smaller cases. Introduces isoclinic QLDP mechanisms based on EITFFs and identifies binary mechanisms as the corresponding high-privacy classical optima.

研究启发

What is the exact closed-form asymptotic ratio Q/C in Theorem 3.1, beyond the abstract-level lower bound Q/C>=3/2? How restrictive are the EITFF existence requirements for implementing the optimal QLDP mechanisms at concrete alphabet sizes n? Do the moderate-privacy numerical indications lead to provable optimality or only to examples of advantage? How sensitive are the results to the assumed utility class, especially the required quadratic Taylor structure of the quantum extension?

限制与不确定性

Results are asymptotic in the high-privacy regime, so practical relevance outside epsilon -> 0 is uncertain. Some quantum mechanism existence/density assumptions around EITFF parameters are not fully resolved, limiting generality. Primary category is quant-ph, so it may be less urgent for a cs.IT workflow unless quantum privacy is a priority.

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