Multipartite Entanglement Routing as a Hypergraph Immersion Problem

• URL: http://arxiv.org/abs/2406.13452v2
• Date: Thu, 19 Dec 2024 08:47:00 GMT
• Title: Multipartite Entanglement Routing as a Hypergraph Immersion Problem
• Authors: Yu Tian, Yuefei Liu, Xiangyi Meng,
• Abstract summary: Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs) Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing. Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs.
• Score: 4.3301675903966625
• License:
• Abstract: Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs). Creating reliable, large-scale multipartite entanglement requires entanglement routing, a process that combines local, short-distance connections into a long-distance connection, which can be considered as a transformation of network topology. Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing. Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs. This generalized hypergraph immersion problem introduces a partial order between QN topologies, permitting certain topological transformations while precluding others, offering discerning insights into the design and manipulation of higher-order network topologies in QNs.

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