Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters

2026-09-11

AI Summary

本文解决了在存在干扰参数情况下最优哈密顿量参数估计问题，通过引入有效生成器并提供明确的最优协议来实现目标参数的精确估计。

Abstract

In many sensing applications, the quantity of interest is not the only unknown, there are also additional unknown parameters, known as nuisance parameters, that affect the precision of estimation. While the ultimate local precision limit for a target parameter is well understood in the absence of nuisance parameters, the problem becomes significantly more challenging when they are present. In this work, we develop a framework for optimal Hamiltonian parameter estimation in the presence of nuisance parameters. We introduce an effective generator that captures the influence of nuisance parameters on the target precision, providing an explicit characterization of the ultimate precision limit for estimating the target parameter. Finally, we provide explicit optimal protocols, including probe state, control, and measurement that saturate this fundamental limit.

Problem

• Hamiltonian parameter estimation
• nuisance parameters
• precision limit

Innovation

• Hamiltonian parameter estimation
• nuisance parameters
• effective generator
• precision limit
• optimal protocols