  In this paper, we examine and compare two fundamentally different
teleportation schemes; the well-known continuous variable scheme by Vaidman,
Braunstein and Kimble (VBK), and a recently proposed hybrid scheme by Andersen
and Ralph (AR). We analyze the teleportation of ensembles of arbitrary pure
single-mode Gaussian states using these schemes and see how they fare against
the optimal measure-and-prepare strategies -- the benchmarks. In the VBK case,
we allow for non-unit gain tuning and consider a class of possibly non-Gaussian
resources in order to optimize performance. The results suggest that the AR
scheme may likely be a more suitable candidate for beating the benchmarks in
the teleportation of squeezing, capable of achieving this for moderate
resources in comparison to the VBK scheme. Moreover, our quantification of
resources, whereby different protocols are compared at fixed values of the
entanglement entropy or the mean energy of the resource states, brings into
question any advantage due to non-Gaussianity for quantum teleportation of
Gaussian states.
