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

Abstract

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 $\Omega (\log \log n)$ qubits each.

35 pages, 5 figures. Quantum journal submission. DOI links for all references

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Cited by in corpus (1)

• Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size