The quantum internet holds promise for performing quantum communication, suchas quantum teleportation and quantum key distribution, freely between anyparties all over the globe. For such a quantum internet protocol, a generalfundamental upper bound on the performance has been derived [K. Azuma, A.Mizutani, and H.-K. Lo, arXiv:1601.02933]. Here we consider its converseproblem. In particular, we present a protocol constructible from any givenquantum network, which is based on running quantum repeater schemes in parallelover the network. The performance of this protocol and the upper bound restrictthe quantum capacity and the private capacity over the network from both sides.The optimality of the protocol is related to fundamental problems such asadditivity questions for quantum channels and questions on the existence of agap between quantum and private capacities.
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