# A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg $XY$ model

## TL;DR

This paper compares local quantum Fisher information and local quantum uncertainty in the Heisenberg XY model, revealing that LQFI detects more quantum correlations than LQU in different magnetic field scenarios.

## Contribution

It provides a comparative analysis of LQFI and LQU in the Heisenberg XY model, highlighting the dominance of LQFI in quantifying quantum correlations.

## Key findings

- LQFI bounds LQU in phase estimation.
- LQFI detects more quantum correlations than LQU.
- Results are consistent across anisotropic and isotropic XY models.

## Abstract

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in the multi-component quantum system [S. Kim et al., Phys. Rev. A. 97, 032326 (2018)]. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg $XY$ model. Two distinct situations are considered. The first one concerns the anisotropic $XY$ model and the second situation concerns the isotropic $XY$ model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.