Optimal quantum metrology with restricted controls
Abstract
Quantum control can enhance sensing precision, but practical protocols are constrained by probe preparation and the available control resources. Optimizing the sensing protocol within these constraints helps establish what precision is experimentally attainable. We study quantum metrology from a fixed initial probe state under restricted Hamiltonian controls with bounded amplitudes. Building on Pontryagin's maximum principle, we formulate quantum Fisher information maximization at a prescribed interrogation time for multiple control channels subject to a weighted amplitude constraint. The formulation also accommodates stochastic Hamiltonian evolution and time-local master equations. A geometric description of sensitivity accumulation reveals the mechanisms underlying the optimized protocols. Two spin-1/2 examples demonstrate the resulting enhancement: time-dependent control outperforms optimized constant control in transverse-field sensing, while optimized waveforms improve upon CPMG pulses for AC-field sensing under strong colored noise. These findings highlight the importance of optimizing sensing protocols within available control resources to improve experimentally attainable precision.
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BibTeX
@misc{sun2026optimal,
title = {{Optimal quantum metrology with restricted controls}},
author = {Li Sun and Haoze Wang and Chong Chen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07583},
eprint = {2611.07583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07583},
}
RIS
TY - UNPB
TI - Optimal quantum metrology with restricted controls
AU - Li Sun
AU - Haoze Wang
AU - Chong Chen
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07583
UR - https://arxiv.org/abs/2611.07583
AB - Quantum control can enhance sensing precision, but practical protocols are constrained by probe preparation and the available control resources. Optimizing the sensing protocol within these constraints helps establish what precision is experimentally attainable. We study quantum metrology from a fixed initial probe state under restricted Hamiltonian controls with bounded amplitudes. Building on Pontryagin's maximum principle, we formulate quantum Fisher information maximization at a prescribed interrogation time for multiple control channels subject to a weighted amplitude constraint. The formulation also accommodates stochastic Hamiltonian evolution and time-local master equations. A geometric description of sensitivity accumulation reveals the mechanisms underlying the optimized protocols. Two spin-1/2 examples demonstrate the resulting enhancement: time-dependent control outperforms optimized constant control in transverse-field sensing, while optimized waveforms improve upon CPMG pulses for AC-field sensing under strong colored noise. These findings highlight the importance of optimizing sensing protocols within available control resources to improve experimentally attainable precision.
ER -