Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^{kd}$$.

We study maximally entangled bases in bipartite systems $$\mathbb {C}^d \otimes \mathbb {C}^{kd}\ (k\in Z^{+})$$ , which are mutually unbiased. By systematically constructing maximally entangled bases, we present an approach in constructing mutually unbiased maximally entangled bases. In particular, five maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{4}$$ and three maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{6}$$ that are mutually unbiased are presented. [ABSTRACT FROM AUTHOR]