Thirty-six quantum officers are entangled
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917308294758400 |
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| author | Ball, Simeon Simoens, Robin |
| author_facet | Ball, Simeon Simoens, Robin |
| contents | There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers does not have a solution. However, it has a "quantum solution": there exist so-called entangled quantum Latin squares of order six [Rather et al., 2022]. We prove that mutually orthogonal quantum Latin squares of order six do not exist if entanglement is not allowed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thirty-six quantum officers are entangled Ball, Simeon Simoens, Robin Quantum Physics Combinatorics 05B15, 05C62, 81P70 There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers does not have a solution. However, it has a "quantum solution": there exist so-called entangled quantum Latin squares of order six [Rather et al., 2022]. We prove that mutually orthogonal quantum Latin squares of order six do not exist if entanglement is not allowed. |
| title | Thirty-six quantum officers are entangled |
| topic | Quantum Physics Combinatorics 05B15, 05C62, 81P70 |
| url | https://arxiv.org/abs/2603.02334 |