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A protocol for transferring an unknown single qubit state has quantumfeatures when the average fidelity of the outcomes is greater than 2/3. We usethe probabilistic and unambiguous state extraction scheme as a mechanism toredistribute the fidelity in the outcome of the teleportation when the processis performed with an X-state as a noisy quantum channel. We show that theentanglement of the channel is necessary but not sufficient in order for thetotal average fidelity f_X to display quantum features, i.e., we find athreshold C_X for the concurrence of the channel. If the mechanism forredistributing fidelity is successfully applied then we find a filtrableoutcome with normalized average fidelity f_{X,USE,0} greater than f_X. Inaddition, we find the threshold concurrence of the channel C_{X,USE,0} in orderfor the normalized average fidelity to display quantum features. Surprisingly,we find that the threshold concurrence C_{X,USE,0} can be lesser than C_X.Finally, we show that if the mechanism for redistributing fidelity fails thenthe respective filtrable outcome has average fidelity lesser than 2/3.

Entanglement thresholds for displaying the quantum nature of teleportation