  We analyze the statistics of observables in continuous variable quantum
teleportation in the formalism of the characteristic function. We derive
expressions for average values of output state observables in particular
cumulants which are additive in terms of the input state and the resource of
teleportation. Working with Squeezed Bell-like states, which may be optimized
in a free parameter for better teleportation performance we discuss the
relation between resources optimal for fidelity and for different observable
averages. We obtain the values of the free parameter which optimize the central
momenta and cumulants up to fourth order. For the cumulants the distortion
between in and out states due to teleportation depends only on the resource. We
obtain optimal parameters for the second and fourth order cumulants which do
not depend on the squeezing of the resource. The second order central momenta
which is equal to the second order cumulants and the photon number average are
optimized by the same resource. We show that the optimal fidelity resource,
found in reference (Phys. Rev. A {\bf 76}, 022301 (2007)) to depend also on the
characteristics of input, tends for high squeezing to the resource which
optimizes the second order momenta. A similar behavior is obtained for the
resource which optimizes the photon statistics which is treated here using the
sum of the squared differences in photon probabilities of input and output
states as the distortion measure. This is interpreted to mean that the
distortions associated to second order momenta dominates the behavior of the
output state for large squeezing of the resource. Optimal fidelity and optimal
photon statistics resources are compared and is shown that for mixtures of Fock
states they are equivalent.
