Strong Asymptotic Composition Theorems for Mutual Information Measures

We characterize the growth of the Sibson and Arimoto mutual informations and
$\alpha $
-maximal leakage, of any order that is at least unity, between a random variable and a growing set of noisy, conditionally independent and identically-distributed observations of the random variable. Each of these measures increases exponentially fast to a limit that is order- and measure-dependent, with an exponent that is order- and measure-independent.