Universal Quantum Magnetometry with Spin States at Equilibrium

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. A general expression is derived for the ultimate achievable precision, as given by the quantum Fisher information. The optimal observable is shown to correspond to the spin projection along a temperature-dependent direction, and allows a maximally precise parameter estimation also through ensemble measurements. Finally, we prove the robustness of our scheme against deviations of the measured spin projection from optimality