Mutually Unbiasedness between Maximally Entangled Bases and Unextendible Maximally Entangled Systems in $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}}$.

The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)$ are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in $\mathbb {C}^{2}\otimes \mathbb {C}^{4}$ and $\mathbb {C}^{2}\otimes \mathbb {C}^{8}$, respectively. [ABSTRACT FROM AUTHOR]