Approaching the Limit in Multiparameter AC Magnetometry with Quantum Control

TL;DR

This paper presents a quantum control protocol that overcomes fundamental limitations in multiparameter AC magnetometry, enabling simultaneous optimal estimation of amplitude and frequency of magnetic fields.

Contribution

The authors introduce a novel control method that orthogonalizes generators to resolve singularities in quantum Fisher information, improving multiparameter estimation.

Findings

Successfully removes singularity in QFIM for joint parameter estimation

Achieves optimal scaling of precision for both parameters simultaneously

Experimental validation with nitrogen-vacancy centers in diamond

Abstract

Simultaneously estimating multiple parameters at the ultimate limit is a central challenge in quantum metrology, often hindered by inherent incompatibilities in optimal estimation strategies. At its most extreme, this incompatibility culminates in a fundamental impossibility when the quantum Fisher information matrix (QFIM) becomes singular, rendering joint estimation unattainable. This is the case for a canonical problem: estimating the amplitude and frequency of an AC magnetic field, where the generators are parallel to each other. Here, we introduce a quantum control protocol that resolves this singularity. Our control protocol strategically engineers the sensor's time evolution so the generators for the two parameters become orthogonal. It not only removes the singularity but also restores the optimal scaling of precision with interrogation time for both parameters simultaneously. We experimentally validate this protocol using a nitrogen-vacancy center in diamond at room temperature, demonstrating the concurrent achievement of the optimal scaling for both parameters under realistic conditions.