  A characteristic function (CF) based formalism for the representation of
quantum optical operations pertaining to the Continuous Variable (CV) quantum
teleportation protocol for general resource and input states is introduced;
allowing for modifications of basic CV teleportation; such as lossy homodyne
measurements and the presence of thermal noise. The output state CF is given as
a product of the CFs of resource and input. The use of non-Gaussian resources
is studied by means of a general class of two-mode squeezed Bell-like states
that include as special cases Gaussian, non-Gaussian and "degaussified"
resources; it is shown that Bell-like resources optimized ("tailored") for
maximum fidelity yield a remarkable improvement in fidelity of teleportation
for the studied input states. A further generalization is introduced with
two-mode squeezed superpositions of Fock states including finite truncations of
Gaussian states as special cases; it is shown that the optimization for maximum
fidelity reduces these resources to truncated Gaussian states. Another class of
non-Gaussian resources is introduced, optimized squeezed cat-like states; their
performance is shown to be higher than that of a Gaussian state; but lower than
that for the Bell-like states. It is shown that the optimal non-Gaussian
resources are those that most closely realize the simultaneous maximization of
the entanglement, the affinity with the two-mode squeezed vacuum and the
(suitably measured) amount of non-Gaussianity. The teleportation of coherent
state inputs is studied using squeezed Bell-like and squeezed cat-like states
superimposed over Gaussian modes representing thermal noise; it is shown that
the optimized non-Gaussian resources are more robust in the presence of noise
then Gaussian resources.
