In this work, maximal $\alpha$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an adversary's maximal expected $\alpha$-gain using optimal measurement is characterized by measured conditional R\'enyi entropy. This can be viewed as a parametric generalization of K\"onig et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the $\alpha$-leakage and maximal $\alpha$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured R\'enyi capacity, respectively. Various properties of maximal $\alpha$-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized $\alpha$-leakage and regularized maximal $\alpha$-leakage for identical and independent quantum privacy mechanisms coincide with $\alpha$-tilted sandwiched R\'enyi information and sandwiched R\'enyi capacity, respectively.

翻译：本文引入最大α-泄露概念，用于量化量子对手在通过量子隐私机制观测数据扰动版本时，能够获取关于数据中任意敏感信息的最大信息量。首先证明，对手通过最优测量获得的最大期望α-增益可由测量条件Rényi熵刻画，这一结果可视为König等人著名猜测概率公式[IEEE Trans. Inf. Theory, 55(9), 2009]的参数化推广。进一步证明，量子隐私机制的α-泄露和最大α-泄露分别由测量Arimoto信息与测量Rényi容量决定。同时建立了最大α-泄露的多种性质，包括数据处理不等式与组合性质。此外，研究表明，独立同分布量子隐私机制的正则化α-泄露与正则化最大α-泄露分别等价于α倾斜夹层Rényi信息与夹层Rényi容量。