  We show how to simplify the computation of the entanglement of formation and
the relative entropy of entanglement for states, which are invariant under a
group of local symmetries. For several examples of groups we characterize the
state spaces, which are invariant under these groups. For specific examples we
calculate the entanglement measures. In particular, we derive an explicit
formula for the entanglement of formation for UU-invariant states, and we find
a counterexample to the additivity conjecture for the relative entropy of
entanglement.
