Nonclassical correlation dynamics of Heisenberg XYZ states with ( <i>x, y</i> )-spin--orbit interaction, <i>x</i> -magnetic field, and intrinsic decoherence effects

Abstract In quantum information, it is important to recognize the effects of additional interactions, such as spin–orbit interactions, on the quantum information resources of two-qubit Heisenberg states. Therefore, we study the nonlocal correlation dynamics affected by the intrinsic decoherence of the spin–spin-Heisenberg-XYZ interaction, which is supported by spin–orbit interactions (Dzyaloshinsky–Moriya) of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>x</m:mi> </m:math> x and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>y</m:mi> </m:math> y directions together. The two spins are coupled to an external inhomogeneous magnetic field (EIMF) in the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>x</m:mi> </m:math> x -direction. We investigate and compare the nonclassical correlation dynamics of local quantum Fisher information, local quantum uncertainty, and log-negativity. The results show that spin–spin and spin–orbit interactions have a high capability to enhance non-local correlations in the presence of an external magnetic field. The enhanced non-local correlation can be further improved by strengthening the spin–spin and spin–orbit interactions, as well as by increasing the EIMF’s inhomogeneity and uniformity, which increases the amplitudes and fluctuations of the generated non-local correlation oscillations. The degradation of non-local correlations due to intrinsic decoherence can be controlled by spin–spin interactions. These degradation correlations can be enhanced by increasing the intensities of spin–orbit interactions, as well as by increasing the EIMF’s inhomogeneity and uniformity.