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

Continuous variable teleportation with Non-Gaussian resources in the characteristic function representation