Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3. We propose to use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity fX to display quantum features, i.e., we find a threshold CX for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity fX,0 that can be greater than fX. In addition, we find the threshold concurrence of the channel CX,0 in order for the average fidelity fX,0 to display quantum features and surprisingly, the threshold concurrence CX,0 can be less than CX. Even more, we find some special cases for which the threshold values become zero.