  The standard benchmark for teleportation is the average fidelity of
teleportation and according to this benchmark not all states are useful for
teleportation. It was recently shown however that all entangled states lead to
non-classical teleportation, with there being no classical scheme able to
reproduce the states teleported to Bob. Here we study the operational
significance of this result. On the one hand we demonstrate that every
entangled state is useful for teleportation if a generalization of the average
fidelity of teleportation is considered which concerns teleporting quantum
correlations. On the other hand, we show the strength of a particular entangled
state and entangled measurement for teleportation -- as quantified by the
robustness of teleportation -- precisely characterizes their ability to offer
an advantage in the task of subchannel discrimination with side information.
This connection allows us to prove that every entangled state outperforms all
separable states when acting as a quantum memory in this discrimination task.
Finally, within the context of a resource theory of teleportation, we show that
the two operational tasks considered provide complete sets of monotones for two
partial orders based upon the notion of teleportation simulation, one
classical, and one quantum.
