  Quantum teleportation establishes a correspondence between an entangled state
shared by two separate par- ties that can communicate classically and the
presence of a quantum channel connecting the two parties. The standard
benchmark for quantum teleportation, based on the average fidelity between the
input and output states, indicates that some entangled states do not lead to
channels which can be certified to be quantum. It was re- cently shown that if
one considers a finer-tuned witness, then all entangled states can be certified
to produce a non-classical teleportation channel. Here we experimentally
demonstrate a complete characterization of a new family of such witnesses, of
the type proposed in Phys. Rev. Lett. 119, 110501 (2017) under different con-
ditions of noise. Furthermore, we show non-classical teleportation using
quantum states that can not achieve average teleportation fidelity above the
classical limit. Our results have fundamental implications in quantum
information protocols and may also lead to new applications and quality
certification of quantum technologies.
