Further results on 2-uniform states arising from irredundant orthogonal arrays
Yajuan Zang, Guangzhou Chen, Kejun Chen, Zihong Tian · Advances in Mathematics of Communications · 2020
The notion of an irredundant orthogonal array (IrOA) was introduced by Goyeneche and \begin{document}$ \dot{Z} $\end{document} yczkowski who showed an IrOA \begin{document}$ _{\lambda}(t, k, v) $\end{document} corresponds to a \begin{document}$ t $\end{document} -uniform state of \begin{document}$ k $\end{document} subsystems with local dimension \begin{document}$ v $\end{document} (Physical Review A. 90 (2014), 022316). In this paper, we construct some kinds of 2-uniform states by establishing the existence of IrOA \begin{document}$ _{\lambda}(2, 5, v) $\end{document} for any integer \begin{document}$ v\geq 4 $\end{document} , \begin{document}$ v eq 6 $\end{document} ; IrOA \begin{document}$ _{\lambda}(2, 6, v) $\end{document} for any integer \begin{document}$ v\geq 2 $\end{document} ; IrOA \begin{document}$ _{\lambda}(2, q, q) $\end{document} and IrOA \begin{document}$ _{\lambda}(2, q+1, q) $\end{document} for any prime power \begin{document}$ q >3 $\end{document} .