  Multipartite quantum correlations, in spite of years of intensive research,
still leave many questions unanswered. While bipartite entanglement is
relatively well understood for Gaussian states, the complexity of mere
qualitative characterization grows rapidly with increasing number of parties.
Here, we present two schemes for transformations of multipartite permutation
invariant Gaussian states by Gaussian local operations and classical
communication. To this end, we use a scheme for possible experimental
realization, making use of the fact, that in this picture, the whole N -
partite state can be described using two separable modes. Numerically, we study
entanglement transformations of tripartite states. Finally, we look at the
effect our protocols have on fidelity of assisted quantum teleportation and
find that while adding correlated noise does not affect the fidelity at all,
there is strong evidence that partial non-demolition measurement leads to a
drop in teleportation fidelity.
