  Quantum teleportation is a method for utilizing quantum measurements and the
maximally entangled Einstein-Podolsky-Rosen (EPR) pair to transmit an unknown
quantum state. It is well known that all entangled states demonstrate so-called
"nonclassical teleportation" that cannot be simulated by the seminal classical
measure-prepare strategy. Herein, we propose a new benchmark which reveals that
not all nonclassical teleportations are truly quantum-mechanical. Rather, there
exists a more robust classical-teleportation model, which includes the
measure-prepare mimicry as a special case, that can describe certain
nonclassical teleportations. Invalidating such a general classical model
indicates genuine quantum teleportation wherein both the pair state and the
measurement are truly quantum-mechanical. We prove that EPR steering empowers
genuine quantum teleportations, rather than entanglement. The new benchmark can
be readily used in practical experiments for ensuring that genuine quantum
teleportation is implemented. The results presented herein provide strict
criteria for implementing quantum-information processing where genuine quantum
teleportation is indispensable.
