Unextendible Maximally Entangled Bases in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$

Abstract

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$($p\le q$) based on the constructions of UMEBs in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ and in ${\mathbb{C}}^p\otimes {\mathbb{C}}^q$, which generalizes the results in [Phys. Rev. A. 94, 052302 (2016)] by two approaches. Two different 48-member UMEBs in ${\mathbb{C}}^6\otimes {\mathbb{C}}^9$ have been constructed in detail.