Can you infer the capability of a network in distributed teleportation by just counting the path length? Yes you can. You may understand the capability of a quantum network in distributed teleportation globally by a single metric. We show that the average of the maximum teleportation fidelities between all pairs of nodes in a large quantum repeater network is a measure of the resourcefulness of the network . It can be used for arbitrary topologies, with and without loops. As examples, we consider topologies (the star, the chain, some trees, and also the ring and the complete graph) with links being simple Werner state-based models. We consider three (semi)realistic scenarios for our analysis. In addition to identifying the parameter ranges for quantum advantages that can be achieved by the network, we also show the large-𝑁 behaviors.
