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

TL;DR

This study analytically explores how a two-qubit system can be used for precise quantum estimation of a magnetic field's azimuthal direction, analyzing the effects of various interactions and field strengths on quantum Fisher information.

Contribution

It provides an exact analytical solution for quantum Fisher information in a two-qubit model with antisymmetric exchange, revealing strategies for optimal magnetic field direction estimation.

Findings

QFI saturation occurs under strong rotating fields.

Estimating azimuthal direction is more efficient with a single qubit when the field is weak.

Using only the unaffected qubit can sometimes outperform local interaction strategies.

Abstract

In this paper, we address the adiabatic technique for quantum estimation of the azimuthal orientation of a magnetic field. Exactly solving a model consisting of a two-qubit system, where one of which is driven by a static magnetic field while the other is coupled with the magnetic field rotating adiabatically, we obtain the analytical expression of the quantum Fisher information (QFI). We investigate how the two-qubit system can be used to probe the azimuthal direction of the field and analyze the roles of the intensities of the magnetic fields, Dzyaloshinskii-Moriya interaction, spin-spin coupling coefficient, and the polar orientation of the rotating field on the precision of the estimation. In particular, it is illustrated that the QFI trapping or saturation may occur if the qubit is subjected to a strong rotating field. Moreover, we discuss how the azimuthal direction of the rotating field can be estimated using only the qubit not affected by that field and investigate the conditions under which this strategy is more efficient than use of the qubit locally interacting with the adiabatically rotating field. Interestingly, in the one-qubit scenario, it was found that when the rotating field is weak, the best estimation is achieved by subjecting the probe to a static magnetic field.