Reasonable method to extract Fisher information from experimental data

Fisher information (FI) plays a crucial role in quantum precision measurement and entanglement detection. Recently two methods have been suggested to extract it from experimental data: Hellinger distance and Kullback-Leibler entropy. In this paper, an extensive investigation is considered with the help of a dichotomic measurement model. It is found that the general quadratic fitting for FI with both methods has two constraints: one is the critical visibility V0=2∕3, the other is the smallest δθ for the dichotomic measurement. To relax them, we propose the higher-order fitting (fourth order considered), by which a reasonable FI is obtained from recent optical experimental data.