Local Quantum Fisher Information In Heisenberg Spin System

Quantum Fisher information is an important concept in quantum metrics,used to measure the parameter information contained in a parametric random variable.Local quantum Fisher information is an optimized definition based on observations related to one of the subsystems,and can be used to measure the accuracy of quantum parameter estimation based on quantum Fisher information.Moreover,local quantum Fisher information provides a tool for measuring quantum correlations of quantum discord types.In recent years,people have conducted extensive research on local quantum Fisher information from multiple perspectives.However,research on local quantum Fisher information in Heisenberg systems mostly focuses on systems with dual lattice spin of 1/2,and there is a lack of research on high-dimensional,multi lattice Heisenberg spin systems.Therefore,based on two important types of Heisenberg model,this paper mainly studies the relevant properties of the local quantum Fisher information in the multi lattice and high spin dimension Heisenberg spin chain model.We studied the variation of local quantum Fisher information with parameters in the "dimeric" Heisenberg chain model,analytically calculated the intrinsic problem of the four particle case,and the analytical expression of local quantum Fisher information in this model.We numerically calculated the variation of different parameters and discussed the results in detail.We studied the variation of local Fisher information with coupling parameters and found that local Fisher information is positively correlated with the interaction strength between two lattice points,while negatively correlated with the coupling strength between surrounding lattice points.In addition,we investigated the effect of temperature on local quantum Fisher information and found that an increase in temperature significantly reduces local Fisher information.We also studied the XXZ mixed spin Heisenberg model,calculated its eigen problem for the two lattice(1/2,1)mixed spin case and analytically calculated the expression of local quantum Fisher information.At the same time,we investigated the relationship between minimum local quantum Fisher information and quantum discord,and applied local quantum Fisher information to study quantum correlations in multi lattice mixed spin systems.We found that in high-dimensional situations,local Fisher information can effectively describe quantum correlations of quantum discord types.Different spin dimensions result in different local Fisher information,which reflects the asymmetry of quantum correlations of quantum discord types for local systems of different dimensions.The coupling situation of surrounding lattice points,as well as the distance between two lattice points,will significantly change the local Fisher information.Compared to the original definition of quantum discord,the calculation of the minimum local quantum Fisher information is much simpler because it does not require optimization of all local generalized measurements.