Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters
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.
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BibTeX
@misc{hu2026optimal,
title = {{Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters}},
author = {Zhiyao Hu and Haidong Yuan and Liang Jiang and Zain H. Saleem},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12857},
eprint = {2609.12857},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12857},
}
RIS
TY - UNPB
TI - Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters
AU - Zhiyao Hu
AU - Haidong Yuan
AU - Liang Jiang
AU - Zain H. Saleem
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12857
UR - https://arxiv.org/abs/2609.12857
AB - 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.
ER -