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arXiv · 2403.14450

Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms

Bo-Yu Yang·Hsuan Yu·Hao-Chung Cheng
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Abstract

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.

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Bo-Yu Yang, Hsuan Yu, Hao-Chung Cheng. 2024-03-21. Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms. https://arxiv.org/abs/2403.14450

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