  We study the holographic dual of a two parameter family of quantities known
as the $\alpha$-$z$ divergences. Many familiar information theoretic quantities
occur within this family, including the relative entropy, fidelity, and
collision relative entropy. We find explicit bulk expressions for the boundary
divergences to second order in a state perturbation whenever $\alpha$ is an
integer and $z\geq0$, as well as when $z\in\{0,\infty\}$ and $\alpha\in
\mathbb{R}$. Our results apply for perturbations around an arbitrary background
state and in any dimension, under the assumption of the equality of bulk and
boundary modular flows.
