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

• DOI: 10.48550/arxiv.2211.06497
• Publication Date: 2022-01-01
• Authors: Sergey Bravyi; Yash Sharma; Márió Szegedy; Ronald de Wolf
• Keywords: Disjoint sets; LOCC; Constant (computer programming)

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 parties. We give constructions such where is not too far optimal $n/2$ while individual parties need to hold only a constant number qubits. In special case when each party holds one qubit, describe family $n$-qubit with proportional $\log n$ based on Reed-Muller codes, as well small numerically found examples for $k=2$ and $k=3$. also prove some lower bounds, example showing that if $k=n/2$ then must have at least $Ω(\log\log n)$ qubits each.