We study the construction of mutually unbiased bases such that all the bases are unextendible maximally entangled ones. By using some results from the theory of finite fields, we construct mutually unbiased unextendible maximally entangled bases in some bipartite systems of higher dimension: \({\mathbb {C}}^{4} \otimes {\mathbb {C}}^{5}\), \({\mathbb {C}}^{6} \otimes {\mathbb {C}}^{7}\), \({\mathbb {C}}^{10} \otimes {\mathbb {C}}^{11}\) and \({\mathbb {C}}^{12} \otimes {\mathbb {C}}^{13}\), which extend the known result of \({\mathbb {C}}^{2} \otimes {\mathbb {C}}^{3}\). We also generalize these results to more bipartie systems of specific dimension.

我们研究互不偏基的构造，以使所有基都是不可扩展的最大纠缠基。通过使用有限域理论的一些结果，我们在一些更高维的二分系统中构造了互不偏且不可扩展的最大纠缠基：\（{\ mathbb {C}} ^ {4} \ otimes {\ mathbb {C}} ^ {5} \），\（{\ mathbb {C}} ^ {6} \ otimes {\ mathbb {C}} ^ {7} \），\（{\ mathbb {C}} ^ {10} \ otimes {\ mathbb {C}} ^ {11} \）和\（{\ mathbb {C}} ^ {12} \ otimes {\ mathbb {C}} ^ {13} \），这扩展了\的已知结果（{\ mathbb {C}} ^ {2} \ otimes {\ mathbb {C}} ^ {3} \）。我们还将这些结果推广到更具体的两方系统。