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

• URL: http://arxiv.org/abs/2211.06497v5
• Date: Thu, 9 May 2024 02:26:17 GMT
• Title: Generating $k$ EPR-pairs from an $n$-party resource state
• Authors: Sergey Bravyi, Yash Sharma, Mario Szegedy, Ronald de Wolf,
• Abstract summary: We show that LOCC protocols can create EPR-pairs between any $k$ disjoint pairs of parties. We also prove some lower bounds, for example showing that if $k=n/2$ then the parties must have at least $Omega(loglog n)$ qubits each.
• Score: 5.617510227362658
• License: http://creativecommons.org/licenses/by/4.0/
• 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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