  In this work, we consider the following teleportation protocol: There is an
arbitrary two-qubit resource state, shared between two spatially separated
parties, Alice and Bob. Applying local unitary operators, they transform the
resource state into the canonical form. To teleport an unknown qubit, Alice now
measures her qubits in the Bell basis. Then, the measurement outcome is
communicated by Alice to Bob via noisy classical channel(s). Finally, after
receiving the classical message, Bob applies the necessary unitary operator to
his qubit. Under this protocol, we find the exact formulae of teleportation
fidelity and its deviation. We further find conditions for non-classical
fidelity within this protocol. If the classical communication is noiseless in
the above protocol then there are resource states which can lead to zero
fidelity deviation. However, we show that such states may not lead to zero
fidelity deviation when the classical communication is noisy in the same
protocol. We also explore the opposite case, i.e., the states, which cannot
lead to zero fidelity deviation in the above protocol when the classical
communication is noiseless, may lead to zero fidelity deviation when the
classical communication is noisy in the same protocol without compromising the
non-classical fidelity. Moreover, we exhibit scenarios within the present
protocol, where the fidelity deviation increases if the entanglement of the
resource state is increased.
