Quantum state estimation with nuisance parameters

TL;DR

This paper reviews quantum state estimation when nuisance parameters are present, extending classical bounds and providing tools to improve estimation accuracy in quantum tomography and metrology.

Contribution

It systematically formulates quantum estimation with nuisance parameters, extends quantum Cramer-Rao bounds, and introduces a parameter orthogonalization method.

Findings

Extended quantum Cramer-Rao bounds to nuisance parameter scenarios

Developed a parameter orthogonalization technique for quantum estimation

Focused on one-parameter estimation with nuisance parameters

Abstract

In parameter estimation, nuisance parameters refer to parameters that are not of interest but nevertheless affect the precision of estimating other parameters of interest. For instance, the strength of noises in a probe can be regarded as a nuisance parameter. Despite its long history in classical statistics, the nuisance parameter problem in quantum estimation remains largely unexplored. The goal of this article is to provide a systematic review of quantum estimation in the presence of nuisance parameters, and to supply those who work in quantum tomography and quantum metrology with tools to tackle relevant problems. After an introduction to the nuisance parameter and quantum estimation theory, we explicitly formulate the problem of quantum state estimation with nuisance parameters. We extend quantum Cramer-Rao bounds to the nuisance parameter case and provide a parameter orthogonalization tool to separate the nuisance parameters from the parameters of interest. In particular, we put more focus on the case of one-parameter estimation in the presence of nuisance parameters, as it is most frequently encountered in practice.