  This paper considers a problem of quantum communication between parties that
are connected through a network of quantum channels. The model in this paper
assumes that there is no prior entanglement shared among any of the parties,
but that classical communication is free. The task is to perfectly transfer an
unknown quantum state from a source subsystem to a target subsystem, where both
source and target are formed by ordered sets of some of the nodes. It is proved
that a lower bound of the rate at which this quantum communication task is
possible is given by the classical min-cut max-flow theorem of network coding,
where the capacities in question are the quantum capacities of the edges of the
network.
