All entangled states can demonstrate non-classical teleportation. (arXiv:1607.03249v2 [quant-ph] UPDATED)

Quantum teleportation, the process by which Alice can transfer an unknown
quantum state to Bob by using pre-shared entanglement and classical
communication, is one of the cornerstones of quantum information. The standard
benchmark for certifying quantum teleportation consists in surpassing the
maximum average fidelity between the teleported and the target states that can
be achieved classically. According to this figure of merit, not all entangled
states are useful for teleportation. Here we propose a new benchmark that uses
the full information available in a teleportation experiment and prove that all
entangled states can implement a quantum channel which can not be reproduced
classically. We introduce the idea of non-classical teleportation witness to
certify if a teleportation experiment is genuinely quantum and discuss how to
quantify this phenomenon. Our work provides new techniques for studying
teleportation that can be immediately applied to certify the quality of quantum

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