arXiv
Open Access
2025
Quantum Latin squares with all possible cardinalities
Ying Zhang
Xin Wang
Lijun Ji
Abstrak
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two unit vectors $|u\rangle, |v\rangle\in \mathcal{H}_n$ are regarded as identical if there exists a real number $θ$ such that $|u\rangle=e^{iθ}|v\rangle$; otherwise, they are considered distinct. The cardinality $c$ of a QLS$(n)$ is the number of distinct vectors in the array. In this paper, we use sub-QLS$(4)$s to prove that for any integer $m\geq 2$ and any integer $c\in [4m,16m^2]\setminus \{4m+1\}$, there is a QLS$(4m)$ with cardinality $c$.
Topik & Kata Kunci
Penulis (3)
Y
Ying Zhang
X
Xin Wang
L
Lijun Ji
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓