  We consider a scenario where a party, say, Alice prepares a pure two-qubit
(either maximally entangled or non-maximally entangled) state and sends one
half of this state to another distant party, say, Bob through a qubit (either
unital or non-unital) channel. Finally, the shared state is used as a
teleportation channel. In this scenario, we focus on characterizing the set of
qubit channels in terms of the final state's efficacy as a resource of quantum
teleportation (QT) in terms of maximal average fidelity and fidelity deviation
(fluctuation in fidelity values over the input states). Importantly, we point
out the existence of a subset of qubit channels for which the final state
becomes useful for universal QT (having maximal average fidelity strictly
greater than the classical bound and having zero fidelity deviation) when the
initially prepared state is either useful for universal QT (i.e., for maximally
entangled state) or not useful for universal QT (i.e., for a subset of
non-maximally entangled pure states). Interestingly, in the latter case, we
show that non-unital channels (dissipative interactions) are more effective
than unital channels (non-dissipative interactions) in producing useful states
for universal QT from non-maximally entangled pure states.
