Challenges in certifying quantum teleportation: moving beyond conventional fidelity benchmark

Abstract: The conventional certification method for quantum teleportation protocols relies on surpassing the highest achievable classical average fidelity between target and teleported states. Our investigation highlights the limitations of this approach: inconsistent conclusions can be obtained when it is considered different distance measures in the quantum state space, leading to contradictory interpretations. In particular, this behavior is manifested when modeling a very common noisy experimental scenario, in which the resource state takes the form of a Werner state generated by the influence of a depolarizing channel acting on the Bell state resource. Two additional noise models, based on amplitude-damping channel, are also analyzed. Our work, therefore, stresses the necessity of new certification methods for quantum teleportation.