双数态输入型M-Z干涉仪中量子相位的最大似然估计和贝叶斯分析

本文采用最大似然估计和贝叶斯分析两种方法，对双数态输入型马赫-曾德尔干涉仪中的量子相位估计进行研究.通过对干涉仪输出端粒子数差和宇称进行理论计算和数值模拟，发现采用贝叶斯分析和粒子数差测量的组合，可以在全相位空间实现最优测量，即待估相位精度达到由量子克拉美罗下界所给定的测量极限，同时，利用贝叶斯分析进行相位估计所需样本数较最大似然估计更少.在通过宇称测量进行相位估计的研究中，发现无法利用贝叶斯分析实现相位估计，但可采用最大似然估计进行研究.借助蒙特卡洛数值模拟分析，我们验证了理论计算结果，即相位估计精度会随待估相位θ₀的变化而改变，将其与粒子数差测量结果对比，进一步确认了粒子数差测量方案的优越性.

Maximum Likelihood estimation and Bayesian analysis of quantum phase in a twin-Fock state input M-Z interferometer

Maximum Likelihood estimation and Bayesian analysis are exploited to study the quantum phase estimation in a twin-Fock state input Mach-Zehnder (M-Z) interferometer. After the theoretical and numerical calculation of particle-number difference measurement and parity measurement at the output of M-Z interferometer, the Bayesian analysis combined with particle-number difference measurement is found to be the best scheme for the optimal phase estimation, and the precision attains the quantum measurement limit given by quantum Cramer-Rao Lower Bound in full phase space. Meanwhile, the number of sample needed in Bayesian analysis is less than Maximum Likelihood estimation. In the study of parity measurement, Bayesian analysis is found unsuitable for phase estimation, but Maximum Likelihood estimation is fine. With the Monte Carlo simulation of the specific phase estimation, the theoretical result is verified, i.e., the precision of phase estimation will change with the change of estimated phase. Compared with the result of particle-number difference measurement, we further confirm the superiority of the particle-number difference measurement.