Total variance and invariant information in complementary measurements

作     者：Bin Chen Shao-Ming Fei Bin Chen;Shao-Ming Fei

作者机构：College of Mathematical ScienceTianjin Normal UniversityTianjin 300387China School of Mathematical SciencesCapital Normal UniversityBeijing 100048China Max-Planck-Institute for Mathematics in the SciencesD-04103 LeipzigGermany 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2020年第72卷第6期

页      面：65-69页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 070201[理学-理论物理] 0704[理学-天文学] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11805143 and 11675113 Beijing Municipal Commission of Education under Grant No.KZ201810028042。 

主　　题：total variance mutually complementary measurements Brukner–Zeilinger invariant information 

摘      要：We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively,we show that the Brukner–Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained.These results provide an operational link between the previous interpretations of the Brukner–Zeilinger invariant information.