arXiv subjects
Publications and source records attributed to Yuyuan Zhang.
In this paper, we investigate the existence of pairs of orthogonal quantum Latin squares, each with maximal cardinality. Using characters and full-rank factorizations of finite abelian groups, together with a product construction, we establish two infinite families of orders for which such pairs exist.
In this paper we investigate the existence of a maximal-cardinality \(t\)-resolvable quantum Latin square (\(t\text{-}\text{RQLS}(v)\)). We determine the existence of a maximal-cardinality \(1\text{-}\text{RQLS}(v)\) with \(17\) possible exceptions based on the established research result and construct a maximal-cardinality \(2\text{-}\text{RQLS}(n^2)\) for every integer \(n\geq6\).
In this paper, we show that for any integer \(v \ge 8\) with \(v \ne 9,11,23\), a quantum Latin square of order $v$ exists for every cardinality \(c \in [v,\,v^{2}] \setminus \{\,v+1\,\}\).