Optimal teleportation fidelity and its deviation in noisy scenarios

In this work, we study quantum teleportation, a fundamental protocol of quantum physics. In particular, we present a mathematical methodology to study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. We describe a teleportation protocol where an arbitrary two-qubit state in canonical form is used as a resource. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and conveys the measurement outcome to Bob via noisy classical channel(s). We derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both can be noisy. To provide the proof of optimality, we provide a systematic method. We further find conditions for non-classical fidelity and dispersion-free teleportation for our teleportation protocol. In this way, we identify noisy environments where it is possible to achieve dispersion-free teleportation without compromising non-classical fidelity. We also demonstrate scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation - a counter-intuitive instance. Finally, we discuss about the minimum classical communication cost required to achieve non-classical fidelity for our protocol. Here we mainly focus on a possible way to optimize the classical communication cost.