Universal representation of the long-range entanglement in the family of Toric Code states
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911136883933184 |
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| author | Zarei, Mohammad Hossein Haghighi, Mohsen Rahmani |
| author_facet | Zarei, Mohammad Hossein Haghighi, Mohsen Rahmani |
| contents | Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we introduce such a representation for the family of Toric Code states by using Kitaev's Ladders as building blocks. We consider Toric Code states corresponding to various planar graphs and apply non-local dientanglers to qubits corresponding to non-contractible cycles that satisfy a topological constraint. We demonstrate that, independent of the geometry of the underlying graph, disentanglers convert Toric Code states into a tensor product of Kitaev's Ladder states. Since Kitaev's Ladders with arbitrary geometric configurations include the short-range entanglements, we conclude that the above universal and non-local pattern of entanglement between ladders is responsible of the long-range entanglement inherent in Toric Code states. Our result emphasizes in the capability of such non-local representations to describe topological order in ground-state wave functions of topological quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal representation of the long-range entanglement in the family of Toric Code states Zarei, Mohammad Hossein Haghighi, Mohsen Rahmani Quantum Physics Strongly Correlated Electrons Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we introduce such a representation for the family of Toric Code states by using Kitaev's Ladders as building blocks. We consider Toric Code states corresponding to various planar graphs and apply non-local dientanglers to qubits corresponding to non-contractible cycles that satisfy a topological constraint. We demonstrate that, independent of the geometry of the underlying graph, disentanglers convert Toric Code states into a tensor product of Kitaev's Ladder states. Since Kitaev's Ladders with arbitrary geometric configurations include the short-range entanglements, we conclude that the above universal and non-local pattern of entanglement between ladders is responsible of the long-range entanglement inherent in Toric Code states. Our result emphasizes in the capability of such non-local representations to describe topological order in ground-state wave functions of topological quantum systems. |
| title | Universal representation of the long-range entanglement in the family of Toric Code states |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2509.03422 |