  We prove a quantum ergodic restriction theorem for the Cauchy data of a
sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a
Riemannian manifold $(M, g)$. The technique of proof is to use a Rellich type
identity to relate quantum ergodicity of Cauchy data on $H$ to quantum
ergodicity of eigenfunctions on the global manifold $M$. This has the
interesting consequence that if the eigenfunctions are quantum unique ergodic
on the global manifold $M$, then the Cauchy data is automatically quantum
unique ergodic on $H$ with respect to operators whose symbols vanish to order
one on the glancing set of unit tangential directions to $H$.
