## 1 Introduction  
The recent growth of the quantum technology has promulgated the preservation of the quantum correlation to become a central problem [1; 2; 3; 4; 5]. The investigations of the non-local correlations (NLCs) (including measurement-induced disturbance [6], quantum discord [7; 8], and the geometrical correlations of measurement-induced nonlocality [9] and skew information theory [10]) become the primary roots of the quantum information [1]. The definitions of NLC measures were mainly on the Hilbert-Schmidt norm (2-norm), the skew information theory, and trace norm [11]. These definitions were exalting new types of the NLCs beyond the quantum entanglement (QE), which have generated many investigations [12; 13].  
It was proven that the NLC quantifiers, which, based on the 2-norm, are not proper measures for the NLC, because they encounter the local ancilla problem [14] in which the NLC quantifiers change arbitrarily under local operations on an unmeasured ancilla state. Therefore, two NLC quantifiers (local quantum uncertainty (LQU) [15] and uncertainty-induced quantum nonlocality (UIN) [16]) are recently defined based on the skew information theory [10]. LQU and UIN are used to quantify the minimal and maximal skew information correlations, respectively. If the LQU and UIN are equal, they present the same correlation that is called \"skew-information correlation\" [12].  
Loss of the non-local correlations resulting from the coupling of a two-qubit system to its environment transforms a correlated two-qubit state into a statistical mixture state [17]. As the coupling of a two-qubit system to its environment leads to different types of decoherence as qubit energy and the phase damping. In the phase-damping model, the phase is damped without energy relaxation [18]. The phase-damping prevents or minimizes the effect of the environmental noise in the practical realization of quantum information processes [19].  
Previous studies of the NLCs in a two-qubit Heisenberg XYZ chain were limited to the quantum entanglement (QE) and quantum memory-assisted entropic uncertainty relation [20; 21]. Solid-state quantum systems are the most natural candidates for the qubit based on quantum dots, electronic spin, and optical lattices [22; 23].  
Here, we investigate the non-local correlations for two-qubit Heisenberg XYZ chain that includes a virtual spin Dzyaloshinskii-Moriya interaction, which results from the [PERSON]'s superexchange interaction. Our study is conducted with new NLC quantifiers based on the skew information theory (LQU and UIN) and [PERSON]'s inequality. Therefore, an analytical solution of the two-qubit Heisenberg XYZ model will be found by applying a new method based on the eigenstates and the eigenvalues of the Hamiltonian. Our results show that is possible to control the generated NLCs, the skew information correlation, the [PERSON]'s inequality correlation, and the sudden death/brith. The type of initial state manipulates the unitary interaction between the two qubits.  
In this contribution, the physical model and its density matrix, are introduced in Section 2. NLC functions will be presented in Section 3. The discussions of the non-local correlation dynamics is conferred in Section 4. Finally, we present our conclusions in Section 5.