  We study entanglement entropy in gravity theory with quantum effects. A
simplest model is a two dimensional Einstein-Hilbert action . We use an
$n$-sheet manifold to obtain an area term of entanglement entropy by summing
over all background fields. A strongly coupled conformal field theory is
expected to describe perturbative quantum gravity theory. Thus, we also use two
dimensional conformal field theory to discuss a factorization of a Hilbert
space. We find that a coefficient of a universal term of the entanglement
entropy is independent of a choice of an entangling surface in two dimensional
conformal field theory for one interval and also argue the result possibly be
extended to multiple intervals. Finally, we discuss that translational
invariance possibly be a necessary condition in a quantum gravity theory by
ruing out a volume law of entanglement entropy.
