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...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11805143 and 11675113Beijing Municipal Commission of Education under Grant No.KZ201810028042。
文摘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.
