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