Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted much attention in recent years. In the paper, we try to construct MUMEBs in \({\mathbb {C}}^{2^s}\otimes {\mathbb {C}}^{2^s}\) by using Galois rings, which is different from the work in [17], where finite fields are used. As applications, we obtain several new types of MUMEBs in \({\mathbb {C}}^{2^s}\otimes {\mathbb {C}}^{2^s}\) and prove that \(M(2^s,2^s)\ge 3(2^s-1)\), which raises the lower bound of \(M(2^s,2^s)\) given in [16].

中文翻译：

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通过使用Galois环构造$$ {\ mathbb {C}} ^ {2 ^ s} \ otimes {\ mathbb {C}} ^ {2 ^ s} $$C2s⊗C2s中相互无偏的最大纠缠基

相互无偏的碱基在量子力学和量子信息处理中起着核心作用。作为一类重要的互不偏基，二分系统中的互不偏最大纠缠基（MUMEB）近年来引起了极大的关注。在本文中，我们尝试使用Galois环在\ {{\ mathbb {C}} ^ {2 ^ s} \ otimes {\ mathbb {C}} ^ {2 ^ s} \}中构造MUMEB摘自[17]中的工作，其中使用了有限域。作为应用程序，我们在\（{\ mathbb {C}} ^ {2 ^ s} \ otimes {\ mathbb {C}} ^ {2 ^ s} \}中获得几种新型的MUMEB，并证明\（M（ 2 ^ s，2 ^ s）\ ge 3（2 ^ s-1）\），提高了[16]中给定的\（M（2 ^ s，2 ^ s）\）的下限。