通过量子信息序刻画隐私机制，实现更精确的隐私-效用权衡。
Quantum Information Ordering and Differential Privacy
- 定义量子态间信息序，统一多类散度关系
- 给出量子参数估计中费舍尔信息的紧上界
- 适用于需严格隐私保障的量子算法设计
我们通过定义量子态对间信息量的顺序关系，研究量子差分隐私（QDP）。特别地，若一对量子态的假设检验散度支配另一对，则该支配关系对所有f-散度均成立。该方法完全刻画了(ε,δ)-QDP机制，识别出最具信息性的(ε,δ)-DP量子态对。据此分析了私有化假设检验与私有化量子参数估计的精确极限，包括在QDP下量子费舍尔信息的紧上界。最后，建立了针对曲棍球棒散度的近最优差分私有量子信道压缩界。
原文摘要 · Abstract (English)
We study quantum differential privacy (QDP) by defining a notion of the order of informativeness between pairs of quantum states. In particular, we show that if the hypothesis testing divergence of one pair dominates over that of the other pair, then this dominance holds for every $f$-divergence. This approach completely characterizes $(\varepsilon,δ)$-QDP mechanisms by identifying the most informative $(\varepsilon,δ)$-DP quantum state pairs. We apply this to study precise limits for privatized hypothesis testing and privatized quantum parameter estimation, including tight upper-bounds on the quantum Fisher information under QDP. Finally, we establish near-optimal contraction bounds for differentially private quantum channels with respect to the hockey-stick divergence.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。