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.

中文翻译：

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Cd ⊗ Cq(d+1) 中相互无偏不可扩展的最大纠缠碱基

基于互无偏基（MUB）的量子测量通常用于量子信息处理。首先，我们在二分系统中构建了两个完整的不可扩展的最大纠缠碱基（UMEB）[公式：见正文]。从而得到这两个UMEBs发展为MUB的充要条件。最后，我们提出了一些在具体的二分系统中相互无偏见的 UMEB。这些结果提供了一种构建最佳测量基础的方法。