Invariant information and quantum state estimation

The invariant information, introduced by C. Brukner and A. Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)], is reconsidered from the point of view of quantum state estimation. We show that this quantity 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 information loses its invariant character.