Constructing UMEB from maximally entangled basis

Abstract

A new way of constructing unextendible maximally entangled basis (UMEB) from 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 $(qd{)}^2-q(d^2-N)$-member UMEB in ${\mathbb{C}}^{qd}\otimes {\mathbb{C}}^{qd}$ for any $q\in \mathbb{N}$. This improves the results in [Phys. Rev. A 90, 034301(2014)], which shows that there exists a $(qd{)}^2-(d^2-N)$-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.

5 pages, some minor errors are corrected

References in corpus (5)

• Entanglement detection
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$
• Unextendible entangled bases with fixed Schmidt number
• Entangled bases with fixed Schmidt number
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$