Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.01972 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918113488928768 |
|---|---|
| author | Zang, Yajuan Zheng, Meihui Tian, Zihong Shan, Xiuling |
| author_facet | Zang, Yajuan Zheng, Meihui Tian, Zihong Shan, Xiuling |
| contents | A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$. The cardinality of a QLS($v$) is the number of its vectors distinct up to a global phase, which is the crucial indicator for distinguishing between classical QLSs and non-classical QLSs. In this paper, we investigate the possible cardinalities of a QLS($v$). As a result, we completely resolve the existence of a QLS($v$) with maximal cardinality for any $v\geq 4$. Moreover, based on Wilson's construction and Direct Product construction, we establish some possible cardinality range of a QLS($v$) for any $v\geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cardinalities of quantum Latin squares Zang, Yajuan Zheng, Meihui Tian, Zihong Shan, Xiuling Combinatorics Mathematical Physics A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$. The cardinality of a QLS($v$) is the number of its vectors distinct up to a global phase, which is the crucial indicator for distinguishing between classical QLSs and non-classical QLSs. In this paper, we investigate the possible cardinalities of a QLS($v$). As a result, we completely resolve the existence of a QLS($v$) with maximal cardinality for any $v\geq 4$. Moreover, based on Wilson's construction and Direct Product construction, we establish some possible cardinality range of a QLS($v$) for any $v\geq 4$. |
| title | On the cardinalities of quantum Latin squares |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2508.01972 |