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In this paper, we address the adiabatic technique for quantum estimation ofthe azimuthal orientation of a magnetic field. Exactly solving a modelconsisting of a two-qubit system, where one of which is driven by a staticmagnetic field while the other is coupled with the magnetic field rotatingadiabatically, we obtain the analytical expression of the quantum Fisherinformation (QFI). We investigate how the two-qubit system can be used to probethe azimuthal direction of the field and analyze the roles of the intensitiesof the magnetic fields, Dzyaloshinskii-Moriya interaction, spin-spin couplingcoefficient, and the polar orientation of the rotating field on the precisionof the estimation. In particular, it is illustrated that the QFI trapping orsaturation may occur if the qubit is subjected to a strong rotating field.Moreover, we discuss how the azimuthal direction of the rotating field can beestimated using only the qubit not affected by that field and investigate theconditions under which this strategy is more efficient than use of the qubitlocally interacting with the adiabatically rotating field. Interestingly, inthe one-qubit scenario, it was found that when the rotating field is weak, thebest estimation is achieved by subjecting the probe to a static magnetic field.

Adiabatic Quantum Estimation: A Numerical Study of the Heisenberg XX Model with Antisymmetric Exchange