Parameter Estimation with Dzyaloshinskii-Moriya Interaction under External Magnetic Fields

TL;DR

This paper investigates how external magnetic fields and Dzyaloshinskii-Moriya interaction influence the precision of parameter estimation in a two-spin XX model, revealing conditions that enhance or reduce estimation accuracy.

Contribution

It demonstrates how magnetic fields and DM interaction affect quantum Fisher information, providing insights into optimizing parameter estimation in spin systems.

Findings

Magnetic fields and DM interaction increase estimation precision.

Inhomogeneous magnetic field b and D have similar effects.

Simultaneous presence of b and B or D and B decreases precision.

Abstract

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.