  Given a certain amount of entanglement available as a resource, what is the
most efficient way to accomplish a quantum task? We address this question in
the relevant case of continuous variable quantum teleportation protocols
implemented using two-mode Gaussian states with a limited degree of
entanglement and energy. We first characterize the class of single-mode
phase-insensitive Gaussian channels that can be simulated via a
Braunstein--Kimble protocol with non-unit gain and minimum shared entanglement,
showing that infinite energy is not necessary apart from the special cases of
the quantum limited attenuator and amplifier. We also find that, apart from the
identity, all phase-insensitive Gaussian channels can be simulated through a
two-mode squeezed state with finite energy, albeit with a larger entanglement.
We then consider the problem of teleporting single-mode coherent states with
Gaussian-distributed displacement in phase space. Performing a geometrical
optimization over phase-insensitive Gaussian channels, we determine the maximum
average teleportation fidelity achievable with any finite entanglement and for
any realistically finite variance of the input distribution.
