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MiS Preprint

Total variance and invariant information in complementary measurements

Bin Chen and Shao-Ming Fei


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.

Mar 17, 2020
Mar 17, 2020

Related publications

2020 Repository Open Access
Bin Chen and Shao-Ming Fei

Total variance and invariant information in complementary measurements

In: Communications in theoretical physics, 72 (2020) 6, p. 065106