Quantum Multi-Parameter Estimation Near Criticality in Ising-XXZ Diamond Structure

Quantum Fisher information (QFI) is frequently utilized to investigate quantum criticality in various spin-chain models. However, little attention has been given to the quantum Fisher information matrix (QFIM) in this context. This study examines criticality and the strategy for the simultaneous estimation of multiple parameters using the QFIM in an Ising-XXZ diamond structure at finite temperatures. Our findings demonstrate that by analyzing the finite-temperature scaling behavior, the variances derived from the QFIM can accurately estimate the critical point in this model. Additionally, we observe that the behavior of variances is contingent upon both the system structure and the parameters used. Moreover, whether the multi-parameter simultaneous estimation strategy is advantageous over individual parameter estimation depends on the system structure, temperature, and the parameters applied.