In this work, we study the structure and cardinality of maximal sets of commuting and anticommuting Paulis in the setting of the abelian Pauli group. We provide necessary and sufficient conditions for anticommuting sets to be maximal and present an efficient algorithm for generating anticommuting sets of maximum size. As a theoretical tool, we introduce commutativity maps and study properties of maps associated with elements in the cosets with respect to anticommuting minimal generating sets. We also derive expressions for the number of distinct sets of commuting and anticommuting abelian Paulis of a given size.

中文翻译：

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关于最大通勤和反通勤的Pauli算子

在这项工作中，我们研究了在阿贝尔保利小组中设置的最大通勤和反通勤宝利斯集的结构和基数。我们为反通勤集最大化提供了必要和充分的条件，并提出了一种用于生成最大大小的反通勤集的有效算法。作为一种理论工具，我们介绍了交换性图并研究了与反集合最小生成集相关的与陪集中的元素关联的图的属性。我们还推导了给定大小的通勤和反通勤阿贝尔保利的不同集合数的表达式。