Schmidt rank constraints in quantum information theory

Can vectors with low Schmidt rank form mutually unbiased bases? high positive under partial transpose states? In this work, we address these questions by presenting several new results related to constraints and their compatibility other properties. We provide an upper bound on the number of bases $$\mathbb {C}^m\otimes \mathbb {C}^n$$ $$(m\le n)$$ formed rank. particular, product cannot exceed $$m+1$$ , which solves a conjecture proposed McNulty et al. Then, show how create entangled state from any supported antisymmetric space numbers are exactly related. Finally, that operator 3 states $$\mathcal {M}_m\otimes \mathcal {M}_n\ (m\le invariant left $$m-2$$ .