Trade-off relations between two-qubit coherence and intrinsic concurrence for Heisenberg XYZ states induced by intrinsic decoherence model

Abstract

This work investigates the trade-off relations between intrinsic concurrence, concurrence, first-order coherence, and total purity for generated two-qubit Heisenberg XYZ states due to spin–spin interactions supported by spin–orbit interactions in the $x$ and $y$ directions with an external inhomogeneous magnetic field in the $x$ direction by using the Milburn model of intrinsic decoherence. We apply the complementary trade-off relations between quantum resource quantifiers when the two-spin Heisenberg XYZ interactions start with a maximally pure state $(|1_A〉\otimes |1_B〉)$ and a maximally entangled state $\left(\frac{1}{\sqrt{2}}[|1_A〉\otimes |1_B〉+|0_A〉\otimes |0_B〉]\right)$. The results of the trade-off relations provide a reliable theoretical basis for the mutual transformation between quantum resource quantifiers. It is shown that the spin–spin-Heisenberg XYZ and $x$, $y$-spin–orbit interactions have a high capability to generate entanglement and degrade coherence with oscillatory evolutions. The amplitudes and frequencies of the oscillations of the information resources depend on the increase of the applied external inhomogeneous magnetic field, the spin–orbit interactions, and the intrinsic two-spin decoherence. It is found that the stationary quantum information resources generated by intrinsic decoherence depend on the spin–spin, spin–orbit interactions as well as on the applied external inhomogeneous magnetic field in the $x$-direction.