  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.
