  A protocol for transferring an unknown single qubit state has quantum
features when the average fidelity of the outcomes is greater than 2/3. We use
the probabilistic and unambiguous state extraction scheme as a mechanism to
redistribute the fidelity in the outcome of the 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
total average fidelity f_X to display quantum features, i.e., we find a
threshold C_X for the concurrence of the channel. If the mechanism for
redistributing fidelity is successfully applied then we find a filtrable
outcome with normalized average fidelity f_{X,USE,0} greater than f_X. In
addition, we find the threshold concurrence of the channel C_{X,USE,0} in order
for 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 then
the respective filtrable outcome has average fidelity lesser than 2/3.
