Non-invertible symmetries act locally by quantum operations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912108652789760 |
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| author | Okada, Masaki Tachikawa, Yuji |
| author_facet | Okada, Masaki Tachikawa, Yuji |
| contents | Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is to point out that these non-invertible symmetries act on local operators by quantum operations, i.e. completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers--Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of non-invertible symmetry operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-invertible symmetries act locally by quantum operations Okada, Masaki Tachikawa, Yuji High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is to point out that these non-invertible symmetries act on local operators by quantum operations, i.e. completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers--Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of non-invertible symmetry operations. |
| title | Non-invertible symmetries act locally by quantum operations |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2403.20062 |