  We introduce a Gaussian version of the entanglement of formation adapted to
bipartite Gaussian states by considering decompositions into pure Gaussian
states only. We show that this quantity is an entanglement monotone under
Gaussian operations and provide a simplified computation for states of
arbitrary many modes. For the case of one mode per site the remaining
variational problem can be solved analytically. If the considered state is in
addition symmetric with respect to interchanging the two modes, we prove
additivity of the considered entanglement measure. Moreover, in this case and
considering only a single copy, our entanglement measure coincides with the
true entanglement of formation.
