  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.
