Quantum Nonlocality For A Spin Model

Quantum nonlocality is not only an integral part of quantum information theory,but also an important resource of quantum communication.Several measurement-induced nonlocality have been recently proposed.They are important tools for characterizing and quantifying the nonlocality of quantum states.However,in striking contrast to other typical quantum correlations,the differences among measurement-induced nonlocality in two spin systems have not been taken into account.In this paper,we will investigate nonlocality of the spin-1/2 and spin-1 XYZ system,where the nonlocality of the system is described by four measurement-induced nonlocality and the differences among measurement-induced nonlocality are compared.Using numerical and analytical method,we calculate four measurement-induced nonlocality with the interaction and temperature for two spin-1/2 and two spin-1 systems respectively.It is shown that those measurement-induced nonlocality show some similar behaviors at low temperature.For example,approaching absolute zero,in a spin-1/2 system,there are two ground states at low temperatures,but three ground states exist in a spin-1 system.The ground states change with the external parameters of the system,so the measurement-induced nonlocality can be used as an indicator of the change.On the other hand,due to the cross of two or more classical functions in concepts,measurement-induced nonlocality give rise to two turning points.At finite temperatures,quantum nonlocality depends on strongly coupled parameters.However,as the temperature increases,the quantum nonlocality decay to zero,because high temperatures weaken the quantum coherence.This means that the coupling parameters and temperature have obvious effects on the quantum nonlocality.Although all quantities have the similar behaviors in a large ranges of parameter in spin-1/2 and spin-1 system,but in some area,those measurement-induced nonlocality is different.For instance,when the spin-1/2 of the system is in the appropriate temperature,measurement-induced nonlocality based on the trace norm suddenly increases,while others decrease with the coupling parameter increasing.Moreover,when the spin-1 system is in the appropriate temperature,as the coupling parameter increase,measurement-induced nonlocality based on the fidelity suddenly decreases,while others increases.Besides,due to the effect of temperature and coupling parameters,measurement-induced nonlocality based on relative entropy will disappear in some areas.In conclusion,we have investigated the quantum nonlocality of two spin models.The quantum nonlocality depends on the spin-spin interaction,the temperature and the spin-orbit interaction,which helps us to understand the quantum nonlocality and establish a correct standard for the measurement nonlocality.