Constructing the unextendible maximally entangled basis from the maximally entangled basis
Yu Jing Guo · Physical Review A · 2016
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 ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{d}$, then there exists a ${(qd)}^{2}\ensuremath{-}q({d}^{2}\ensuremath{-}N)$-member UMEB in ${\mathbb{C}}^{qd}\ensuremath{\bigotimes}{\mathbb{C}}^{qd}$ for any $q\ensuremath{\in}\mathbb{N}$. This improves the results in Wang et al. [Phys. Rev. A 90, 034301 (2014)], which shows that there exists a ${(qd)}^{2}\ensuremath{-}({d}^{2}\ensuremath{-}N)$-member UMEB in ${\mathbb{C}}^{qd}\ensuremath{\bigotimes}{\mathbb{C}}^{qd}$ provided that an $N$-member UMEB exsits in ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{d}$. In addition, a very easy way of constructing UMEB in ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{{d}^{\ensuremath{'}}}$ with $d<{d}^{\ensuremath{'}}$ is presented, which promotes and covers all the previous related work.