Parameter Estimation with Dzyaloshinskii-Moriya Interaction under External Magnetic Fields

We study the effects of external magnetic fields on the precision of parameter estimation with thermal entanglement of two spins in XX model, in the presence of Dzyaloshinskii-Moriya (DM) interaction. Calculating the quantum Fisher information, we show that homogeneous magnetic field B, inhomogeneous magnetic field b or DM interaction D increases the precision of parameter estimation, overwhelming the destructive effects of thermalization. We also show that for the model in consideration, the effects of b and D are the same. However, the existence of both b and B (or both D and B) decreases the precision. We find that in order to increase the precision in parameter estimation tasks, applying b in the ferromagnetic case and B in the antiferromagnetic case should be preferred.