一种基于弱测量的参量评估方案  

A Scheme for Parameter Estimation Based on Weak Measurement

作　　者：尹霜 於亚飞[2] 张智明[1] YIN Shuang;YU Ya-fei;ZHANG Zhi-ming(Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices,South China Normal University,Guangzhou 510006,China;Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials,South China Normal University,Guangzhou 510006,China)

机构地区：[1]华南师范大学光电学院,微纳光子功能材料与器件重点实验室,广东广州510006 [2]华南师范大学,广东省量子调控工程与材料重点实验室,广东广州510006

出　　处：《量子光学学报》2021年第3期200-206,共7页Journal of Quantum Optics

基　　金：国家自然科学基金(61941501,61775062,11574092,61378012,91121023)。

摘　　要：弱测量过程包括三个主要步骤:初态制备、弱耦合、后选择.这个过程中诸多因素会对耦合参量的评估精度产生影响,本文工作主要探讨当光束的空间自由度与偏振自由度通过双折射晶体耦合时,探针初态的参数(坐标分布的平均值和方差)、耦合常数以及后选择角对耦合参量的评估精度的影响.我们具体通过讨论相关参数对待评估耦合参量Fisher信息的影响,借以分析对耦合参数评估精度的影响.结果表明,在本方案中,(1)增加探针初态坐标分布的方差和坐标的平均值(中心位置)都可以提高后选择概率,并增加总Fisher信息;(2)参量越小,评估精度越高,但相应的后选择概率越低;(3)在满足弱测量近似条件下,系统的后选择态与初态越接近正交,获得的评估精度越高.High-precision parameter estimation plays an important role in modern science and technology.Quantum weak measurement is a technique that can be used to amplify and estimate small parameters.It is of great significance to explore the influence of quantum weak measurement on the precision of parameter estimation.The weak measurement process mainly involves two physical systems:the system and the pointer.This process consists of three main steps:first,preparing the initial state of the system and the pointer;second,the system weakly interacts with the pointer;third,the system is postselected to a final state that is nearly orthogonal to its initial state.Many factors affect the estimation precision of the coupling parameters.In this paper,the influence of the initial state parameters of the pointer(mean and variance of coordinate distribution),coupling constant and post-selection angle on the estimation precision of the coupling parameters are investigated when the spatial degree of freedom and polarized degree of freedom of the beam are coupled through a birefringent crystal.We specifically discuss the influence of relevant parameters on the Fisher information of coupling parameters to be estimated,and analyze the influence on the estimation precision of coupling parameters.The results show that(1)increasing the variance and the mean value(the center position)of the initial state coordinate distribution can improve the post-selection probability and increase the total Fisher information;(2)The smaller the coupling constant,the higher the estimation precision,but the lower the corresponding post-selection probability;(3)Under the condition of weak measurement approximation,the more orthogonal the post-selection state and the initial state of the system are,the higher the estimation precision is.Therefore,we can obtain larger Fisher information about the parameters to be estimated by appropriately adjusting these tunable parameters,that is,to improve the estimation precision of the coupling parameters.

关 键 词：弱测量 参量评估 Fisher信息 

分 类 号：O431[机械工程—光学工程] TM93[理学—光学]