  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.
