【作者】 李浩；

【导师】 程泂；

【作者基本信息】 宁波大学 ， 物理学， 2023， 硕士

【摘要】 随着物理学的发展进入量子时代,人们对提升物理量的测量精度有着极为迫切的需求,于是旨在突破散粒噪声极限的量子度量学应运而生,其也在量子信息学科中占有非常重要的地位。量子相位一般是不可观测的,这就需要使用参数估计理论来相应的进行相位估计。相位估计的极限是Cramér-Rao界,其定义了系统测量数据包含的信息量,称为Fisher信息。在最优测量下,系统本身所能包含的最大信息量便是量子Fisher信息。现已有许多研究利用量子效应提升量子Fisher信息,从而超越标准量子极限以达到海森堡极限。然而对于实验而言,量子耗散不可避免,也就是说整个系统是处在开放环境中的,系统的量子性会随着时间演化而消逝,从而系统的测量精密性会被降低,其也更加难以抗拒量子噪声的影响。另一方面,开放系统中量子体系的演化也会携带部分环境的参数,这使得我们可以利用系统的量子态来对这些参数进行测量,但这些参数往往在各类研究中被经验化处理,这使得目前这类参数的测量精度仍难以取得进展,成为了限制各类应用的短板。本文基于参数估计理论,以量子Fisher信息作为精度的度量形式,以两种开放系统模型为例,对开放系统参数测量精度的提升问题进行讨论。其中一种模型使用了光力系统结合传统的转子陀螺仪装置,利用输入输出关系得到了包含转速测量信息的光学输出矩阵,通过推导得到适用于任意转速的单模高斯量子Fisher信息的显式形式。数值结果表明,通过调节激光使系统靠近不稳定边界,可以得到系统测量转速的最高精度。另一种模型为核磁共振系统,我们通过开放系统量子演化分析了一般的线性系统参数和弛豫时间的测量方案并给出了解析的量子Fisher信息。提出参数估计过程下的提升方案,即使用优化脉冲控制量子比特演化方式来规避噪声,并使用算法以量子Fisher信息作为目标函数将控制优化至最大测量提升的脉冲,从而提升了此体系的开放参数测量精度。更多还原

【Abstract】 As the development of physics enters the quantum era,there is an extremely urgent need to improve the measurement precision of physical quantities,so quantum metrology,which aims to break through the limit of shot noise,was born,and it also occupies a very important position in the discipline of quantum information.The quantum phase is generally unobservable,which requires the use of parameter estimation theory to perform phase estimation accordingly.The limit of phase estimation is the Cramér-Rao bound,which defines the amount of information contained in the measurement data of the system,called Fisher information.The maximum amount of information that the system itself can contain under optimal measurements is the quantum Fisher information.There have been many studies on the use of quantum effects to enhance the quantum Fisher information to exceed the standard quantum limit in order to reach the Heisenberg limit.However,for experiments,quantum dissipation is inevitable,which means that the whole system is in an open environment and the quantum nature of the system will fade with time,thus measurement precision will be reduced and it will be more difficult to resist the effect of quantum noise.Besides,the evolution of the quantum system will also carry some of the parameters of the environment,which allows us to use the quantum state of the system to measure these parameters,but these parameters are often empirically treated in various studies,which makes it difficult to measure these parameters accurately,and it has become an barrier to various applications.In this thesis,we will discuss the problem of improving the sensitivity of open system pa-rameter measurement based on the theory of parameter estimation,using quantum Fisher infor-mation as a form of precision measure,and two open system models as examples.One of the models uses an optomechanical system combined with a conventional rotor gyroscope device to obtain an optical output matrix containing rotational speed measurement information by using the input-output relationship,and the explicit form of the single-mode Gaussian quantum Fisher information applicable to arbitrary rotational speed is obtained by derivation.Numerical results show that the highest precision of the system for measuring rotational speed can be obtained by adjusting the laser so that the system is close to the instability boundary.Another model is the nuclear magnetic resonance system,where we analyze the general linear system parameters and relaxation time measurement scheme by open system quantum evolution and give the resolved quantum Fisher information.We propose a boosting scheme under the parameter estimation pro-cess,i.e.,we use an optimized pulse control quantum bit evolution approach to circumvent noise,and use an algorithm to optimize the control to the maximum measurement boosting pulse using the quantum Fisher information as the objective function,thus improving the open parameter measurement precision of this system.更多还原