二维希尔伯特空间中的参数估计测量不兼容度  

Incompatibility of multiparameter estimation in two-dimensional Hilbert space

作　　者：叶雅婷 陆晓铭 YE Yating;LU Xiaoming(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第4期61-65,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61871162)。

摘　　要：如何描述不对易可观测量之间估计精度的制约关系,是量子多参数估计中的主要难题之一。文章通过由不兼容系数决定的信息遗憾制约关系来揭示多参数估计精度的相互制约。推导得到二维希尔伯特空间中多参数估计不兼容系数的解析表达式,并通过示例分析该解析表达式的可行性。In quantum multiparameter estimation problems,Heisenberg s uncertainty principle forbids the simultaneous attainments of the best estimation precisions for different parameters.Recent work reveals the tradeoff relation between estimation accuracies for different parameters by information regret tradeoff relation,which is determined by the incompatibility coefficient.In this paper,we derive an analytic expression for the incompatibility coefficient in quantum systems whose Hilbert space is two-dimensional and demonstrate its advantage by an example.This analytical expression is helpful to study the multiparameter estimation problem with quantum systems with two-dimensional Hilbert space,e.g.,the photon polarization and electron spin.

关 键 词：量子多参数估计 量子Cramér-Rao界 测不准原理 量子测量 

分 类 号：O431.2[机械工程—光学工程]