  We report our theoretical and experimental investigations into errors in
quantum state estimation, putting a special emphasis on their asymptotic
behavior. Tomographic measurements and maximum likelihood estimation are used
for estimating several kinds of identically prepared quantum states (bi-photon
polarization states) produced via spontaneous parametric down-conversion.
Excess errors in the estimation procedures are eliminated by introducing a new
estimation strategy utilizing Akaike's information criterion. We make a
quantitative comparision between the errors of the experimentally estimated
states and their asymptotic lower bounds, which are derived from the
Cram\'{e}r-Rao inequality. Our results reveal influence of entanglement on the
errors in the estimation. An alternative measurement strategy employing
inseparable measurements is also discussed, and its performance is numerically
explored.
