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Quantum teleportation (QT) serves as one of the building blocks of thecurrent state information science and technology which necessitates propercharacterization of the resources yielding QT. While entanglement is known tobe the basic requirement to achieve QT, condition of sufficiency for QT stillremains an open question. Here, we provide an analytic proof that in the caseof Gaussian entangled resources, in general, Einstein-Podolsky-Rosen (EPR)correlation is {\em sufficient for QT}. For a relatively restricted set ofGaussian states we provide even a tighter condition that EPR correlation is{\em both necessary and sufficient for QT}. Our results, in turn, provide acomplete characterization of the resources required for QT.

Necessary and Sufficient Criteria for Gaussian Quantum Teleportation