The orthogonality speed of two-qubit state interacts locally with spin chain in the presence of Dzyaloshinsky-Moriya interaction

The orthogonality time is examined for different initial states settings interacting locally with different types of spin interaction: $XX$, Ising and anisotropic models. It is shown that, the number of orthogonality increases, and consequently the time of orthogonality decreases as the environment qubits increase. The shortest time of orthogonality is displayed for the $XX$ chain model, while the largest time is shown for the Ising model. The external field increases the numbers of orthogonality, while Dzyaloshinsky-Moriya interaction decreases the time of orthogonality. The initial state settings together with the external field has a significant effect on decreasing/increasing the time of orthogonality

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