  We consider entanglement swapping with general mixed two-mode Gaussian states
and calculate the optimal gains for a broad class of such states including
those states most relevant in communication scenarios. We show that for this
class of states, entanglement swapping adds no additional mixedness, that is
the ensemble average output state has the same purity as the input states. This
implies that, by using intermediate entanglement swapping steps, it is, in
principle, possible to distribute entangled two-mode Gaussian states of higher
purity as compared to direct transmission. We then apply the general results on
optimal Gaussian swapping to the problem of quantum communication over a lossy
fiber and demonstrate that, contrary to negative conclusions in the literature,
swapping-based schemes in fact often perform better than direct transmission
for high input squeezing. However, an effective transmission analysis reveals
that the hope for improved performance based on optimal Gaussian entanglement
swapping is spurious since the swapping does not lead to an enhancement of the
effective transmission. This implies that the same or better results can always
be obtained using direct transmission in combination with, in general, less
squeezing.
