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Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty

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Abstract

We investigate the nonclassical correlations via local quantum Fisher information (LQFI), local quantum uncertainty (LQU) and logarithmic negativity for the two-qubit Ising model under a magnetic field in an arbitrary direction. The nonclassical correlations of LQFI, LQU and LN are explicitly derived when the magnetic field is perpendicular to the direction of the two-qubit Heisenberg Ising model. While when the magnetic field has an arbitrary direction, they are investigated numerically. The closed forms of the LQFI and LQU confirm the inequality between the quantum Fisher information and skew information, where the LQFI is always greater than or equal to the LQU, and both of them show very similar behavior with different amplitudes. It is found that when the system is in its ground state, the LQFI and LQU have the same closed form which can be used in calculating the LN. The dependence of the nonclassical correlations on the direction of the magnetic field is investigated with the effects of the magnitude of the applied magnetic field and the spin interaction coupling. The phenomenon of sudden change for the LQFI and LQU and the sudden death and sudden birth of the entanglement depend on the temperature and the magnitude of the applied magnetic field.

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Acknowledgements

This project was supported financially by the Academy of Scientific Research and Technology (ASRT), Egypt, Grant No 6667, ASRT is the 2nd affiliation of this research.

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Authors and Affiliations

  1. Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt

    R. A. Abdelghany & M. Tammam

  2. Department of Physics, National Chung Hsing University, Taichung, 402, Taiwan

    R. A. Abdelghany

  3. Department of Mathematics, College of Science and Humanities in Al-Aflaj Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia

    A.-B. A. Mohamed

  4. Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

    A.-B. A. Mohamed

  5. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    A.-S. F. Obada

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  1. R. A. Abdelghany
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Correspondence to R. A. Abdelghany.

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Abdelghany, R.A., Mohamed, AB.A., Tammam, M. et al. Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty. Eur. Phys. J. Plus 136, 680 (2021). https://doi.org/10.1140/epjp/s13360-021-01649-9

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