Operational advantages provided by nonclassical teleportation

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 nonclassical 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 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 on the notion of teleportation simulation, one classical and one quantum.

Figure 1

The two operational tasks. Panel (a) presents teleportation of quantum correlations specified by $\mathcal{G}=\{\sigma ,{\xi }_b,f\left(b\right)\}$, where $\sigma$ is the input state, ${\left\{{\xi }_b\right\}}_b$ are the target states and $f\left(b\right)$ is the score given when a correct target state is obtained. Bob is allowed to perform any local quantum simulation of his teleportation instrument $\mathrm{\Lambda }$, i.e., he has access to ${\mathrm{\Lambda }}_b^{\prime }$ of the form (10). Panel (b) shows the task of subchannel discrimination with quantum side information which involves a set of subchannels to discriminate $\mathbb{E}={\left\{{\mathcal{E}}_x\right\}}_x$ and uses quantum resources of the teleportation experiment (bipartite state and measurement).