Multipartite Entanglement Routing as a Hypergraph Immersion Problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915070661885952 |
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| author | Tian, Yu Liu, Yuefei Meng, Xiangyi |
| author_facet | Tian, Yu Liu, Yuefei Meng, Xiangyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multipartite Entanglement Routing as a Hypergraph Immersion Problem Tian, Yu Liu, Yuefei Meng, Xiangyi Quantum Physics Discrete Mathematics Social and Information Networks Computational Physics Physics and Society 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. |
| title | Multipartite Entanglement Routing as a Hypergraph Immersion Problem |
| topic | Quantum Physics Discrete Mathematics Social and Information Networks Computational Physics Physics and Society |
| url | https://arxiv.org/abs/2406.13452 |