Feedback Control And Error Correction For Multi-parameter Estimation Of Open Quantum Systems

Quantum precision measurement,which exploits quantum mechanical effects such as superposition and entanglement,and the high sensitivity of quantum systems to small changes in external signals,provides a higher measurement accuracy than classical metrological schemes.It has been widely used in the field of high-precision measurement and sensing.Parameter estimation is a fundamental task of quantum precision measurement,and improving the accuracy of parameter estimation is one of the main goals of quantum precision measurement.In view of the fact that many practical quantum systems inevitably interact with the external environment,which will spoil coherence and decrease the accuracy of estimation greatly,it is of great significance to study how to improve the parameter estimation accuracy in open quantum systems to promote the development of quantum precision measurement.For multi-parameter quantum estimation,this dissertation will design feedback control and quantum error correction scheme to improve the estimation accuracy of multiple parameters simultaneously.The main contents are summarized as follows:(1)A brief review of the origin and development of quantum multi-parameter estimation is given,and the existing methods to improve the accuracy of multi-parameter estimation,especially feedback control and quantum error correction,are introduced.On this basis,the research contents of this dissertation are introduced.(2)Aiming at multi-parameter estimation of the two-level open quantum system,a feedback control scheme combined with optimal control is proposed,which can effectively improve the accuracy of multi-parameter estimation.Firstly,in view of the incompatibility between parameters,by selecting an appropriate initial probe state,it can be guaranteed that in the case of obtaining the most information for one parameter,the information of another parameter can also be obtained.Secondly,the effectiveness of the feedback control method can be verified by exploring the effects of three quantum feedback operator types on the multi-parameter estimation precision.On this basis,an optimal feedback control method based on gradient ascent algorithm is further proposed.Finally,the effectiveness of the optimal feedback control method can be verified by the simulation experiments,and the superiority of the optimal feedback control scheme can be demonstrated by comparison with the coherent control method.(3)For the multi-parameter estimation of the Hamiltonian in a two-qubit system with spontaneous emission,a quantum error correction scheme combined with feedback control is proposed,which can achieve simultaneous high-precision estimation of multiple parameters while accurately detecting errors.There are two main measurement methods for feedback control.The conditions for achieving the highest estimation accuracy are different for error correction schemes that combine different measurement methods,and these two error correction schemes are designed in turn in this dissertation.Firstly,the optimal initial probe state is determined according to the specific estimation problem,and an appropriate error correction code can be designed according to the probe state.Then,the corresponding feedback operator and driving Hamiltonian are designed by investigating the effects of decoherence on the code space.Finally,in order to achieve the simultaneous high-precision estimation of multiple parameters,in the scheme based on direct photodetection,the additional control need to be introduced to eliminate the incompatibility between multiple parameters;in the scheme based on homodyne detection,it is necessary to introduce a recovery operator that acts on the system to overcome the influence of the frequent jumping process on quantum states in code space.