Near-perfect Noisy Quantum State Teleportation

Achieving high fidelity of quantum teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. To this end, we devise a distinctive protocol for ensuring teleportation fidelity {\it close to unity}, hinging essentially on the timing of Alice's Bell-basis measurement (BM) dependent on the choice of Bob's local noise parameters, but is independent of Alice's local noise. Our scheme is enabled by Alice communicating to Bob only two of the BM outcomes corresponding to the states that are decoherence-free under common dephasing at Alice's wing. On the other hand, Bob is asked to discard the states of his qubit for the other two BM outcomes in order to maximize fidelity of the teleported state. This ensures the teleportation fidelity's independence of noise parameters in Alice's wing. We formulate the protocol in terms of a generic two-level quantum system, subjected to non-Markovian dephasing noise, applicable for any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. Notably, we show that high fidelity is achievable even using resource states with small values of the entanglement measure. Remarkably, even within the local regime of Werner states, where Bell-CHSH inequalities are not violated, the teleportation fidelity remains significantly high. Finally, we discuss the empirical feasibility of our scheme using photonic qubits.