  In this work, we study the combined effects of noisy resource state and noisy
classical communication on teleportation fidelity and its deviation. Basically,
we consider a teleportation protocol, where a general two-qubit state in
canonical form is used as resource, which of course, can be a noisy entangled
state. Thereafter, to teleport an unknown qubit, Alice measures her qubits in
Bell basis and convey the measurement outcome to Bob via noisy classical
channel(s). In particular, we derive the exact formulae of optimal
teleportation fidelity and corresponding fidelity deviation where the resource
state and the classical communication, both of them can be noisy. We further
find conditions for non-classical fidelity and dispersion-free teleportation
within the present protocol. In this way, we identify the noisy environments
where it is possible to achieve the dispersion-free teleportation without
compromising the non-classical fidelity. We also exhibit scenarios where the
increase of entanglement in the resource state, may degrade the quality of
teleportation. Finally, we discuss on minimum classical communication cost
required to achieve non-classical fidelity in our protocol.
