Construction of mutually unbiased bases in Cd⊗C2ld′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$\end{document}

We study mutually unbiased bases in Cd⊗C2ld′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$\end{document}. A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in Cd⊗C2ld′(l∈Z+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$\end{document} from MUMEBs in Cd⊗Cd′(d′=kd,k∈Z+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$\end{document} and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in Cd⊗C2ld′(l∈Z+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$\end{document} from MUUMEBs in Cd⊗Cd′(d′=kd+r,0<r<d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0<r<d)$$\end{document} have been presented. Detailed examples are given.