Many-Body Anticommutator And Its Applications In The Normalization Of Completely Symmetric States With Majorana'S Stellar Representations

Understanding the quantum properties of many-body states is important in the fields of both quantum information and condensed-matter physics. For this purpose, we generalize the basic concept of the anticommutator from two operators to the many-body case. Some key properties are given for the many-body anticommutators, and examples are provided for Pauli operators and density matrices. Using these results and techniques from the symmetry group, in a straightforward way, we give the normalization of the completely symmetric states with Majorana's stellar representations. Our developed method will help to pave the way in the study of many-body symmetric systems.