A New Strategy of Quantum-State Estimation for Achieving the Cramer-Rao   Bound
  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. 
Koji Usami, Yoshihiro Nambu, Yoshiyuki Tsuda, Keiji Matsumoto, and   Kazuo Nakamura