On the Existence of Algebraic Equiangular Lines
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911501173915648 |
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| author | Van Loo, Igor Oggier, Frédérique |
| author_facet | Van Loo, Igor Oggier, Frédérique |
| contents | We consider real and complex equiangular lines, generated by unit vectors. We show that, for an arbitrary dimension $d$, if there exists a set of $d^2$ equiangular unit vectors in $\mathbb{C}^d$, then there must exist a set of $d^2$ equiangular unit vectors with all of their coefficients in a number field. This result is motivated by the question of constructing SIC-POVMs in quantum physics and conjectures around them. We discuss applications of our techniques to the case of real equiangular lines and consequences of the above results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09128 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Existence of Algebraic Equiangular Lines Van Loo, Igor Oggier, Frédérique Quantum Physics Number Theory 81P15 (Primary), 11R04 (Secondary) We consider real and complex equiangular lines, generated by unit vectors. We show that, for an arbitrary dimension $d$, if there exists a set of $d^2$ equiangular unit vectors in $\mathbb{C}^d$, then there must exist a set of $d^2$ equiangular unit vectors with all of their coefficients in a number field. This result is motivated by the question of constructing SIC-POVMs in quantum physics and conjectures around them. We discuss applications of our techniques to the case of real equiangular lines and consequences of the above results. |
| title | On the Existence of Algebraic Equiangular Lines |
| topic | Quantum Physics Number Theory 81P15 (Primary), 11R04 (Secondary) |
| url | https://arxiv.org/abs/2603.09128 |