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.

arXiv:2611.07583 [quant-ph]

(or arXiv:2611.07583v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.07583 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.