Unextendible maximally entangled bases in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}$

TL;DR

This paper proves the existence of unextendible maximally entangled bases (UMEB) in bipartite spaces where dimensions differ, providing explicit constructions and revealing multiple possible sizes of UMEB.

Contribution

It establishes the existence of UMEB in $\

Findings

Existence of UMEB in $\

Multiple UMEB sizes possible

Explicit construction method provided

Abstract

We solved the unextendible maximally entangled basis (UMEB) problem in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}(d\neq d')$,the results turn out to be that there always exist a UMEB.In addition,there might be two sets of UMEB with different numbers.The main difficult is to prove the unextendibility of the set of states.We give an explicit construction of UMEB by considering the Schmidt number of the complementary space of the states we construct.