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arXiv · 2211.06497

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

Sergey Bravyi·Yash Sharma·Mario Szegedy·Ronald de Wolf
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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.

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Sergey Bravyi, Yash Sharma, Mario Szegedy, Ronald de Wolf. 2022-11-11. Generating $k$ EPR-pairs from an $n$-party resource state. https://doi.org/10.22331/q-2024-05-14-1348

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