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

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.