Quantum measurements based on mutually unbiased base (MUB) are commonly used in quantum information processing. Firstly, we construct two completed unextendible maximally entangled bases (UMEBs) in bipartite systems [Formula: see text]. Then, the sufficient and necessary conditions of these two UMEBs develop into MUB can be obtained. Finally, we present some UMEBs that are mutually unbiased in concrete bipartite systems. These results provide a method to construct the best measurement bases.
Unextendible maximally entangled bases in
$${\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}$$
C
pd
⊗
C
qd
