Unextendible Entangled Bases With a Fixed Schmidt Number Based on Generalized Weighing Matrices - Tao, Yuan-Hong; Yong, Xin-Lei; Bai, Ya-Ru; Xu, Dan-Ni; Wu, Shu-Hui (Frontiers in Physics, 2022)
We systematically study the constructions of unextendible entangled bases with fixed Schmidt number k (UEB$k$) in bipartite system $\mathbb{C}^d\otimes\mathbb{C}^{d'}$. Motivated by the methods of [J. Phys. A $52: 375303, 2019]$, we construct $(dd'-v)$-member UEB$k$s in $\mathbb{C}^d\otimes\mathbb{C}^{d'}$ by using generalized weighing matrices, thus generalize the results of [arXiv: $1909.10043, 2020$]. We also present the corresponding expressions of our constructions and graphically illustrate UEB3s in $\mathbb{C}^5\otimes\mathbb{C}^{6}$ and $\mathbb{C}^6\otimes\mathbb{C}^{6}$.