Universal quantum magnetometry with spin states at equilibrium

TL;DR

This paper demonstrates that quantum-enhanced precision in magnetic field estimation can be achieved using spins at thermal equilibrium, with optimal measurement strategies derived from thermodynamic quantities.

Contribution

It introduces a universal approach to quantum magnetometry at equilibrium, deriving the quantum Fisher information and optimal observables based on thermodynamics.

Findings

Quantum Fisher information expressed in thermodynamic terms

Optimal measurement is spin projection along a universal direction

Scheme is robust against measurement deviations

Abstract

We address metrological protocols for the estimation of the intensity and the orientation of a magnetic field, and show that quantum-enhanced precision may be achieved by probing the field with an arbitrary spin at thermal equilibrium. We derive a general expression for the ultimate achievable precision, as given by the quantum Fisher information, and express this quantity in terms of common thermodynamic quantities. We also seek for the optimal observable, and show that it corresponds to the spin projection along a suitable direction, defined by a universal function of the spin temperature. Finally, we prove the robustness of our scheme against deviations of the measured spin projection from optimality.