Asymmetric SICs over finite fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918070396649472 |
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| author | Iverson, Joseph W. Mixon, Dustin G. |
| author_facet | Iverson, Joseph W. Mixon, Dustin G. |
| contents | Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl--Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such \textit{totally asymmetric} SICs exist in infinitely many dimensions in the finite field setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymmetric SICs over finite fields Iverson, Joseph W. Mixon, Dustin G. Metric Geometry Combinatorics Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl--Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such \textit{totally asymmetric} SICs exist in infinitely many dimensions in the finite field setting. |
| title | Asymmetric SICs over finite fields |
| topic | Metric Geometry Combinatorics |
| url | https://arxiv.org/abs/2506.20778 |