Quantum Latin squares with maximal cardinality

Yajuan Zang, Meihui Zheng, Zihong Tian +1 more

Yiwen Zhang, Haitao Cao

In this paper, we prove that there exist a symmetric quantum Latin square with maximal cardinality of order $n$ for all $n\geq 6$, and a symmetric idempotent quantum Latin square with maximal cardinality of order $4k+2$ for all $k\geq 1$.

Roberto Osellame

Mingzhen Lv, Haitao Cao

We construct quantum Latin squares with maximal cardinality and quantum Latin hypercubes with maximal cardinality over the real field.

Alexey Orlovsky

Yuyuan Zhang, Yiwen Zhang, Mingzhen Lv +1 more

ABSTRACT In this paper, by extending the classical singular direct product construction to the quantum setting we resolve the existence problem for quantum Latin squares with maximal cardinality except for 11 possible exceptions. We also prove that there exists a quantum Latin cube of order with maximal cardinality for all positive integers , except when is a prime or , where are prime numbers and .