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

Sergey Bravyi1, Yash Sharma2, Mario Szegedy2, and Ronald de Wolf3

1IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA.
2Rutgers University
3QuSoft, CWI and University of Amsterdam, the Netherlands.

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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.

We describe protocols enabling $n$ parties sharing a fixed entangled resource state $|\psi\rangle$ to create $k$ EPR-pairs shared among any $k$ pairs of parties. The protocols require only local quantum operations and classical communication. We give examples when $k$ is not too far from the optimal $k=n/2$ while each party needs to hold only a constant number of qubits.

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Cited by

[1] Maria Flors Mor-Ruiz and Wolfgang Dür, "Influence of noise in entanglement-based quantum networks", arXiv:2305.03759, (2023).

[2] Nathan Claudet, Mehdi Mhalla, and Simon Perdrix, "Small k-pairable states", arXiv:2309.09956, (2023).

[3] Maxime Cautrès, Nathan Claudet, Mehdi Mhalla, Simon Perdrix, Valentin Savin, and Stéphan Thomassé, "Vertex-minor universal graphs for generating entangled quantum subsystems", arXiv:2402.06260, (2024).

[4] Si-Yi Chen, Jessica Illiano, Angela Sara Cacciapuoti, and Marcello Caleffi, "Entanglement-Based Artificial Topology: Neighboring Remote Network Nodes", arXiv:2404.16204, (2024).

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