A way of constructing the unextendible maximally entangled basis (UMEB) from the maximally entangled basis (MEB) is proposed. Consequently, it is shown that if there is an $N$-member UMEB in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$, then there exists a ${\left(qd\right)}^2-q(d^2-N)$-member UMEB in ${\mathbb{C}}^{qd}\otimes {\mathbb{C}}^{qd}$ for any $q\in \mathbb{N}$. This improves the results in Wang et al. [Phys. Rev. A 90, 034301 (2014)], which shows that there exists a ${\left(qd\right)}^2-(d^2-N)$-member UMEB in ${\mathbb{C}}^{qd}\otimes {\mathbb{C}}^{qd}$ provided that an $N$-member UMEB exsits in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$. In addition, a very easy way of constructing UMEB in ${\mathbb{C}}^d\otimes {\mathbb{C}}^{d^{\prime }}$ with $d<d^{\prime }$ is presented, which promotes and covers all the previous related work.

• Received 18 September 2016

DOI:https://doi.org/10.1103/PhysRevA.94.052302