非厄米哈密顿量中的量子Fisher信息与参数估计  

Quantum Fisher information and parameter estimation in non-Hermitian Hamiltonians

作　　者：李竞 丁海涛 张丹伟 Li Jing;Ding Hai-Tao;Zhang Dan-Wei(Key Laboratory of Atomic and Subatomic Structure and Quantum Control,Ministry of Education,School of Physics,South China Normal University,Guangzhou 510006,China;National Key Laboratory of Solid State Microstructures,School of Physics,Nanjing University,Nanjing 210093,China)

机构地区：[1]华南师范大学物理学院,原子亚原子结构与量子调控教育部重点实验室,广州510006 [2]南京大学物理学院,固体微结构物理国家重点实验室,南京210093

出　　处：《物理学报》2023年第20期161-171,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12174126);广东省基础与应用基础研究基金(批准号:2021A1515010315)资助的课题.

摘　　要：量子Fisher信息给出参数估计的最优精度极限,在量子度量学中有重要的应用.近年来,在量子系统中实现非厄米哈密顿量的理论与实验研究受到广泛关注.本文研究基于非厄米哈密顿量本征态的参数估计,给出其中单参数与两参数估计的量子Fisher信息及其量子Cramér-Rao下界,计算与分析非互易、具有增益-耗散的Su-Schrieffer-Heeger模型,非厄米量子Ising链、拓扑陈绝缘体模型和二能级系统中动量及外场参数估计的量子Fisher信息.结果表明:在这几个非厄米模型中,对于单参数估计,量子Fisher信息在能隙闭合区域和例外点附近显著增大,从而提高参数估计的精度极限;对于两参数估计,量子Fisher信息矩阵的行列式在能隙闭合和例外点附近同样明显增大,拓扑区域比平庸区域的整体评估精度更高,且由陈数确定两参数估计误差的拓扑下界.Quantum Fisher information bounds the ultimate precision limit in the parameter estimation and has important applications in quantum metrology.In recent years,the theoretical and experimental studies of non-Hermitian Hamiltonians realized in quantum systems have attracted wide attention.Here,the parameter estimation based on eigenstates of non-Hermitian Hamiltonians is investigated,and the corresponding quantum Fisher information and quantum Cramér-Rao bound for the single-parameter and two-parameter estimations are given.In particular,the quantum Fisher information about estimating intrinsic momentum and external parameters in the non-reciprocal and gain-and-loss Su-Schrieffer-Heeger models,and non-Hermitian versions of the quantum Ising chain,Chern-insulator model and two-level system are calculated and analyzed.For these non-Hermitian models,the results show that in the case of single-parameter estimation in these non-Hermitian models,the quantum Fisher information increases significantly in the gapless regime and near the exceptional points,which can improve the accuracy limit of parameter estimation.For the two-parameter estimation,the determinant of the quantum Fisher information matrix also increases obviously near the gapless and exceptional points.In addition,a higher overall accuracy can be achieved in the topological regime than in the trivial regime,and the topological bound in two-parameter estimation can be determined by the Chern number.

关 键 词：量子Fisher信息 参数估计 非厄米系统 拓扑态 

分 类 号：O413[理学—理论物理]