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

We systematically study the constructions of unextendible entangled bases with a fixed Schmidt number k (UEBk) in a bipartite system Cd⊗Cd′. Motivated by the methods of [J. Phys. A 52 : 375,303, 2019], we construct (dd’ − v)-member UEBks in Cd⊗Cd′ by using generalized weighing matrices and thus generalize the results of [arXiv: 1909.10043, 2020]. We also present the corresponding expressions of our constructions and graphically illustrate UEB3s in C5⊗C6 and C6⊗C6.