Generating $k$ EPR-pairs From An $n$-party Resource State

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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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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 $Omega(loglog n)$ qubits each.

Popular summary

We describe protocols enabling $n$ parties sharing a fixed entangled resource state $|psirangle$ 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.

► BibTeX data

@article{Bravyi2024generatingkeprpairs, doi = {10.22331/q-2024-05-14-1348}, url = {https://doi.org/10.22331/q-2024-05-14-1348}, title = {Generating {$k$} {EPR}-pairs from an {$n$}-party resource state}, author = {Bravyi, Sergey and Sharma, Yash and Szegedy, Mario and Wolf, Ronald de}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1348}, month = may, year = {2024} }

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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).

The above citations are from SAO/NASA ADS (last updated successfully 2024-05-14 13:10:48). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-05-14 13:10:46: Could not fetch cited-by data for 10.22331/q-2024-05-14-1348 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2024-05-14-1348/

Time Stamp: May 14, 2024

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Republished By Plato

Abstract

Popular summary

► BibTeX data

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