The Weyl Transform of a measure

(1) Suppose $\mu$ is a smooth measure on a hypersurface of positive Gaussian curvature in ${\mathbb{R}}^{2n}$. If $n\ge 2$, then $W(\mu )$, the Weyl transform of $\mu$, is a compact operator, and if $p>n\ge 6$ then $W(\mu )$ belongs to the $p$-Schatten class. (2) There exist Schatten class operators with linearly dependent quantum translates.