Continuous variable versus hybrid schemes for quantum teleportation of Gaussian states

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.