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

Motivated by quantum network applications over classical channels, we initiate the study of n-party resource states from which LOCC protocols can create EPR-pairs between any k disjoint pairs of parties. We give constructions 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. In the 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 prove some lower bounds, for example showing that if k=n/2 then the parties must have at least Ω(loglogn) qubits each.