I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% successful of retrieving the quantum state at the desired location.
In all real experiments I've glanced at and read thoroughly, the fidelities are never 1. Doesn't this suggest that what the experimenters "teleported" was really just a different state? Doesn't the fidelity have to be exactly 1 in order to really remove a quantum state from one location and make it appear at another location?
My concern is that either I've missed something, or that we aren't really teleporting at all because the final state achieved on the other side is not equal to the initial state!