  The effect of non-orthogonality of an entangled non-orthogonal state based
quantum channel is investigated in detail in the context of the teleportation
of a qubit. Specifically, average fidelity, minimum fidelity and minimum
assured fidelity (MASFI) are obtained for teleportation of a single qubit state
using all the Bell type entangled non-orthogonal states known as quasi Bell
states. Using Horodecki criterion, it is shown that the teleportation scheme
obtained by replacing the quantum channel (Bell state) of the usual
teleportation scheme by a quasi Bell state is optimal. Further, the performance
of various quasi Bell states as teleportation channel is compared in an ideal
situation (i.e., in the absence of noise) and under different noise models
(e.g., amplitude and phase damping channels). It is observed that the best
choice of the quasi Bell state depends on the amount non-orthogonality, both in
noisy and noiseless case. A specific quasi Bell state, which was found to be
maximally entangled in the ideal conditions, is shown to be less efficient as a
teleportation channel compared to other quasi Bell states in particular cases
when subjected to noisy channels. It has also been observed that usually the
value of average fidelity falls with an increase in the number of qubits
exposed to noisy channels (viz., Alice's, Bob's and to be teleported qubits),
but the converse may be observed in some particular cases.
