  We experimentally analyzed the statistical errors in quantum-state estimation
and examined whether their lower bound, which is derived from the Cramer-Rao
inequality, can be truly attained or not. In the experiments, polarization
states of bi-photons produced via spontaneous parametric down-conversion were
estimated employing tomographic measurements. Using a new estimation strategy
based on Akaike's information criterion, we demonstrated that the errors
actually approach the lower bound, while they fail to approach it using the
conventional estimation strategy.
