Quantum symmetries of Hadamard matrices
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913236605992960 |
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| author | Gromada, Daniel |
| author_facet | Gromada, Daniel |
| contents | We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size $N\ge 4$ has quantum symmetries and that all Hadamard matrices of a fixed size are mutually quantum isomorphic. These results pass also to the corresponding Hadamard graphs. We also define quantum Hadamard matrices acting on quantum spaces and bring an example thereof over matrix algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02047 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum symmetries of Hadamard matrices Gromada, Daniel Quantum Algebra Mathematical Physics Category Theory 20G42 (Primary), 05C25, 18M25, 18M40 (Secondary) We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size $N\ge 4$ has quantum symmetries and that all Hadamard matrices of a fixed size are mutually quantum isomorphic. These results pass also to the corresponding Hadamard graphs. We also define quantum Hadamard matrices acting on quantum spaces and bring an example thereof over matrix algebras. |
| title | Quantum symmetries of Hadamard matrices |
| topic | Quantum Algebra Mathematical Physics Category Theory 20G42 (Primary), 05C25, 18M25, 18M40 (Secondary) |
| url | https://arxiv.org/abs/2210.02047 |