Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms
<|reference_start|>Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms: 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.<|reference_end|>
@article{yang2024maximal,
    title={Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms},
    author={Bo-Yu Yang, Hsuan Yu, Hao-Chung Cheng},
    journal={arXiv preprint arXiv:2403.14450},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14450},
    primaryClass={quant-ph cs.CR cs.IT math.IT}
}