LAUSR

A special entangled basis (SEBk) is a set with $dd'$ orthonormal entangled pure states in $\mathbb{C}^d \otimes \mathbb{C}^{d'}$ whose nonzero Schmidt coefficients are all equal to $1/\sqrt{k}$. When $k$ is equal to the minimum of $d$ and $d'$, we get a maximally entangled basis. In this paper, we present how to construct a special entangled basis via some special matrices which are known as weighing matrices. Specially, using a skew Hadamard matrix of order $k+1$, we derive a weighing matrix which is useful for constructing SEBk in $\mathbb{C}^d \otimes \mathbb{C}^{d'}$ whenever $\min\{d,d'\}\geq k$. These results are further progress of those studied by Guo \emph{et al.} in [\textcolor[rgb]{0.00,0.07,1.00}{J. Phys. A: Math. Theor. \textbf{48} 245301(2015)}]. We also disprove two conjectures proposed by them.