Incompatibility of optimized protection of entanglement and teleportation fidelity in the presence of decoherence

Entanglement is the key to teleport an unknown quantum state with fidelity higher than classical limit. For decohering open quantum systems, entanglement decreases with the strength of interaction between quantum systems and the environment. As a result, teleportation fidelity decreases. The technique of weak measurement and its reversal help to protect entanglement in the presence of amplitude-damping decoherence. In this work, we have shown that the optimal protection of entanglement measured by concurrence does not always optimize teleportation fidelity in the presence of decoherence modeled by the amplitude damping decoherence. More specifically, when one of the systems interacts with the environment, optimization of entanglement and teleportation fidelity requires different strengths of reverse weak measurement. Here, the success probability of optimal protection of entanglement is higher than the success probability of optimal protection of teleportation fidelity. Interestingly, when both systems interact with the environment, optimization of entanglement implies optimization of teleportation fidelity. Therefore, the resources of quantum teleportation along with entanglement need to be explored.