Study On Physical Problems Of Quantum Parameter Estimation

The current study of quantum information includes three major research fields,quantum communication,quantum computing and quantum precision measurement.Quantum precision measurement becomes a new hot topic recently.The subject of studying parameter estimation precision is called quantum metrology,which plays an important role during the acqusition and transfer of quantum information.The precision of classical unknown parameter estimation is limited by the standard quantum limit(or shot-noise limit).In order to enhance the parameter estimation precision,the quantum properties of probe state have been introduced.This dissertation focuses on the effects of the quantum properties of quantum probe state and quantum opeations on the precision of quantum metrology.The precision of quantum parameter estimation directly relates to the quantum Fisher information of probe state,so it is of great importance to study the intrinsic factors of quantum Fisher information in quantum metrology.Generally speaking,a whole process of quantum parameter estimation includes four steps,i.e.the preparation of probe states,the interaction between the probe system and the unknown parameter system(namely,the parameterization process),the measurement of the output states,and the estimation of unknown parameter based on the measurement results.Among these four septs,quantum properties play prominent roles maily in the first to steps,i.e.the probe state preparation and the parameterization processes,so the study of this dissertation will be focused on these two steps.The tyical quantum properties of a quantum probe state include quantum coherence,quantum entanglement,purity,quantum discord and so on.So far the intrinsic reason why the quantum parameter estimation is superior to its classical counterpart is still not clear for us,which is exactly what we have studied in this dissertation,and a preliminary answer to this problem has been given too.In addition,it is well known that a quantum operation can change the quantum properties of a quantum probe state,which may contribute to the enhancement of the precision of quantum pararmeter estimation,so it is of great importance to study the metrological power of quantum operations and quantum evolutions.It was studied in this dissertation too.The main contributions of this dissertation are summarized as follows:1.The contribution of quantum manipulation processes to quantum Fisher information in quantum metrology was studied,and the metrological power of a quantum operation was defined.Different quantum manipulation processes can change the quantum properties of the probe state,such as quantum coherence,quantum entanglement and purity,which are considered to be closely related to the quantu Fisher information of the probe state,so several quantum manipulation processes,such as single-qubit purification,entanglement purification,and entanglement distillation,have been studied in terms of the quantum properties and the quantum Fisher information of the probe states.The results show that the joint operations during the above-mentioned quantum manipulation processes always play a positive role in enhancing the quantum Fisher information of the probe state.In addition,to quantitatively describe the quantum Fisher information chaning power of a quantum operation we defined the metrological power of a quantum operation.2.In qubit systems,the intrinsic relationship between the quantum coherence of a probe state and its quantum Fisher information was revealed.In general,the measure of quantum coherence is base-dependent,meanwhile the precision of a quantum parameter estimation process depends on the direction(on the Bloch sphere)of the parameterization process.When the reference base of the quantum coherence,i.e.a vector on the Bloch sphere,is equal to the direction vector of the parameterization process,there exists an exact relationship between the quantum coherence of a probe state and its quantum Fisher information,i.e.the square of the quantum coherence equals to the quantum Fisher information.3.It was revealed that the generalized quantum coherence is the physical origin of the precision of quantum parameter estimation.Although we have revealed the exact relationship between the quantum coherence of a probe state and its quantum Fisher information in qubit systems,it cannot be directly generalized to the high-dimensional systems,which indicates that besides the quantum coherence we may need another physical factor to completely characterize quantum Fisher information.Based on the fact that the complete coherece information between two eigenvectors of an observable should include not only the quantum coherce itself but also the eigenvalues of these two eigenvectors,generlized quantum coherence is defined.The results show that there exists an exact relationship between the generalized quantum coherence of a probe state in arbitrary-dimensional system and its quantum Fisher information,i.e.the square of the generalized quantum coherence equals to the quantum Fisher information,which is consistent with the result of the qubit case.Thus we conclude that the generalized quantum coherence is the intrinsic physical origin of the quantum enhancement of parameter estimation.