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Motivated by quantum network applications over classical channels, weinitiate the study of $n$-party resource states from which LOCC protocols cancreate EPR-pairs between any $k$ disjoint pairs of parties. We giveconstructions of such states where $k$ is not too far from the optimal $n/2$while the individual parties need to hold only a constant number of qubits. Inthe special case when each party holds only one qubit, we describe a family of$n$-qubit states with $k$ proportional to $\log n$ based on Reed-Muller codes,as well as small numerically found examples for $k=2$ and $k=3$. We also provesome lower bounds, for example showing that if $k=n/2$ then the parties musthave at least $\Omega(\log\log n)$ qubits each.

Generating $k$ EPR-pairs from an $n$-party resource state