  We determine the quantum variance of a sequence of families of automorphic
forms on a compact quotient arising from a non-split quaternion algebra. Our
results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the
modular curve, whose method required a cusp. Our method uses the theta
correspondence to reduce the problem to the estimation of metaplectic
Rankin--Selberg convolutions. We apply it here to the first non-split case.
