Maximal $\alpha$ - Leakage for Quantum Privacy Mechanisms and Operational Meaning of Measured Renyi Capacity
Part Of
IEEE International Symposium on Information Theory - Proceedings
Start Page
3308
End Page
3313
ISBN (of the container)
979-835038284-6
Date Issued
2024-07-07
Author(s)
Abstract
In this work, maximal a-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 a-gain using optimal measurement is characterized by measured conditional Renyi entropy. This can be viewed as a parametric generalization of Konig et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the a-leakage and maximal -leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured Renyi capacity, respectively. Various properties of maximal a-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized a-leakage and regularized maximal a-leakage for identical and independent quantum privacy mechanisms coincide with a-tilted sandwiched Renyi information and sandwiched Renyi capacity, respectively. A full version of this paper is accessible at: https://arxiv.org/pdf/2403.14450 [1].
Event(s)
2024 IEEE International Symposium on Information Theory (ISIT)
Publisher
IEEE
Type
conference paper