  The invariant information introduced by Brukner and Zeilinger, Phys. Rev.
Lett. 83, 3354 (1999), is reconsidered from the point of view of quantum state
estimation. We show that it is directly related to the mean error of the
standard reconstruction from the measurement of a complete set of mutually
complementary observables. We give its generalization in terms of the Fisher
information. Provided that the optimum reconstruction is adopted, the
corresponding quantity loses its invariant character.
