Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2502.19466 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908439055171584 |
|---|---|
| author | Balasubramanian, Vijay Cummings, Charlie |
| author_facet | Balasubramanian, Vijay Cummings, Charlie |
| contents | We study the patterns of multipartite entanglement in Chern-Simons theory with compact simple gauge group $G$ and level $k$ for states defined by the path integral on ``link complements'', i.e., compact manifolds whose boundaries consist of $n$ topologically linked tori. We focus on link complements which can be described topologically as fibrations over a Seifert surface. We show that the entanglement structure of such fibered link complement states is controlled by a topological invariant, the monodromy of the fibration. Thus, the entanglement structure of a Chern-Simons link state is not simply a function of the link, but also of the background manifold in which the link is embedded. In particular, we show that any link possesses an embedding into some background that leads to Greenberger--Horne--Zeilinger state (GHZ)-like entanglement. Furthermore, we demonstrate that all fibered links with periodic monodromy have GHZ-like entanglement, i.e., a partial trace on any link component produces a separable state. These results generalize to any three dimensional topological field theory with a dual chiral rational conformal field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multipartite Entanglement Structure of Fibered Link States Balasubramanian, Vijay Cummings, Charlie High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics We study the patterns of multipartite entanglement in Chern-Simons theory with compact simple gauge group $G$ and level $k$ for states defined by the path integral on ``link complements'', i.e., compact manifolds whose boundaries consist of $n$ topologically linked tori. We focus on link complements which can be described topologically as fibrations over a Seifert surface. We show that the entanglement structure of such fibered link complement states is controlled by a topological invariant, the monodromy of the fibration. Thus, the entanglement structure of a Chern-Simons link state is not simply a function of the link, but also of the background manifold in which the link is embedded. In particular, we show that any link possesses an embedding into some background that leads to Greenberger--Horne--Zeilinger state (GHZ)-like entanglement. Furthermore, we demonstrate that all fibered links with periodic monodromy have GHZ-like entanglement, i.e., a partial trace on any link component produces a separable state. These results generalize to any three dimensional topological field theory with a dual chiral rational conformal field theory. |
| title | Multipartite Entanglement Structure of Fibered Link States |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2502.19466 |