Generation and robustness of non-local correlations induced by Heisenberg XYZ and intrinsic decoherence models: (x,y)-spin-orbit interactions and $x$- magnetic field

In this work, the Milburn intrinsic decoherence model is used to investigate the role of spin-spin Heisenberg XYZ interaction supported by spin-orbit Dzyaloshinsky Moriya (DM) interactions of x and y directions together in the non-local correlation (NLC) dynamics of Local quantum Fisher information (LQFI), local quantum uncertainty (LQU), and Log-negativity's entanglement. The two-qubit Heisenberg XYZ (non-X) states' nonlocal correlation generations are explored under the effects of the uniformity and the inhomogeneity of an applied x-direction external inhomogeneous magnetic field (EIMF). Our meticulous exploration of the obtained results shows that the spin-spin Heisenberg XYZ and x,y-spin-orbit interactions have a high capability to raise non-local correlations in the presence of a weak external magnetic field. The raised non-local correlation can be improved by strengthening the spin-spin and x,y spin-orbit interactions and increasing the EIMF's inhomogeneity and uniformity. Non-local correlation oscillations' amplitudes and fluctuations are increased. The degradations of the NLCs' generations in the presence of intrinsic decoherence (NLCs' robustness against intrinsic decoherence) can be decreased by strengthening the spin-spin interactions. They can be increased by increasing the intensities of x,y spin-orbit interactions as well as increasing the EIMF's inhomogeneity and uniformity.