AUTHOR=Tao Yuan-Hong , Yong Xin-Lei , Bai Ya-Ru , Xu Dan-Ni , Wu Shu-Hui 

TITLE=Unextendible Entangled Bases With a Fixed Schmidt Number Based on Generalized Weighing Matrices

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.896164

DOI=10.3389/fphy.2022.896164

ISSN=2296-424X

ABSTRACT=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 $\mathbb{C}^6\otimes\mathbb{C}^{6}$.