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On the thermal nonclassical correlations in a two-spin XYZ Heisenberg model with Dzyaloshinskii–Moriya interaction

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Abstract

The quantum correlations between two neighbouring anisotropic XYZ Heisenberg spins under the effect of Dzyaloshinskii–Moriya interaction at thermal equilibrium is considered. We evaluate and compare the negativity, uncertainty-induced quantum nonlocality and local quantum uncertainty corresponding to involved system. By exploiting the behaviour of each quantifier, in terms of the system parameters, we have shown that the uncertainty-induced quantum nonlocality can reveal certain non-classicality that goes beyond negativity and local quantum uncertainty. Further, we show that the presence of Dzyaloshinskii–Moriya interaction along the z-axis can reduce the undesirable destructive effects of thermal fluctuations, and therefore enhances quantum correlations in the two-spin system. In addition, an entangled–unentangled phase transition can be detected from the behaviour of negativity.

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Notes

  1. This applies only to two-qubit X-shaped states [23].

References

  1. E. Schrödinger, Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  2. A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  3. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  4. S.L. Braunstein, H.J. Kimble, Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)

    Article  ADS  Google Scholar 

  5. D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Experimental quantum teleportation. Nature 390, 575 (1997)

    Article  ADS  Google Scholar 

  6. A.K. Ekert, Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  7. B.P. Lanyon, M. Barbieri, M.P. Almeida, A.G. White, Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  8. A. Datta, G. Vidal, Role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75, 042310 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Datta, A. Shaji, C.M. Caves, Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  10. H. Ollivier, W.H. Zurek, Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  11. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  12. L. Henderson, V. Vedral, Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34, 6899 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  13. Y. Huang, Computing quantum discord is NP-complete. New J. Phys. 16, 033027 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  14. S. Luo, S. Fu, Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)

    Article  ADS  Google Scholar 

  15. B. Dakić, V. Vedral, Č. Brukner, Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

  16. D. Girolami, T. Tufarelli, G. Adesso, Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)

  17. S.-X. Wu, J. Zhang, C.-S. Yu, H.-S. Song, Uncertainty-induced quantum nonlocality. Phys. Lett. A 378, 344 (2014)

    Article  ADS  Google Scholar 

  18. E.P. Wigner, M.M. Yanasse, Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  19. S. Luo, Wigner–Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  20. S. Wang, H. Li, X. Lu, G.-L. Long, Closed form of local quantum uncertainty and a sudden change of quantum correlations. arXiv:quant-ph/1307.0576v2

  21. Y. Khedif, M. Daoud, Local quantum uncertainty and trace distance discord dynamics for two-qubit \(X\) states embedded in non-Markovian environment. Int. J. Mod. Phys. B 32, 1850218 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. Y. Khedif, M. Daoud, Pairwise nonclassical correlations for superposition of Dicke states via local quantum uncertainty and trace distance discord. Quantum Inf. Process. 18, 45 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  23. Y. Khedif, M. Daoud, E.H. Sayouty, Thermal quantum correlations in a two-qubit Heisenberg XXZ spin-\(\frac{1}{2}\) chain under an inhomogeneous magnetic field. Phys. Scr. 94, 125106 (2019)

    Article  ADS  Google Scholar 

  24. N. Habiballah, Y. Khedif, M. Daoud, Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinski–Moriya interaction. Eur. Phys. J. D 72, 154 (2018)

    Article  ADS  Google Scholar 

  25. T.-C. Yi, W.-L. You, N. Wu, A.M. Oleś, Criticality and factorization in the Heisenberg chain with Dzyaloshinskii–Moriya interaction. Phys. Rev. B 100, 024423 (2019)

    Article  ADS  Google Scholar 

  26. D. Park, Thermal entanglement and thermal discord in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions. Quantum Inf. Process. 18, 172 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  27. A. Abdel-Aty, N. Zakaria, L.Y. Cheong, N. Metwallay, Quantum network via partial entangled state. J. Commun. 9, 397 (2014)

    Google Scholar 

  28. A. Abdel-Aty, N. Zakaria, L.Y. Cheong, N. Metwally, Effect of the spin–orbit interaction on partial entangled quantum network. Lect. Notes Electr. Eng. 285, 529 (2014)

    Article  Google Scholar 

  29. A. Abdel-Aty, N. Zakaria, L.Y. Cheong, N. Metwally, Entanglement and teleportation via partial entangled-state quantum network. J. Comput. Theor. Nanosci. 12, 2213 (2015)

    Article  Google Scholar 

  30. G.F. Zhang, Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski–Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75, 034304 (2007)

    Article  ADS  Google Scholar 

  31. M. von Helversen, J. Böhm, M. Schmidt, M. Gschrey, J.-H. Schulze, A. Strittmatter, S. Rodt, J. Beyer, T. Heinde, S. Reitzenstein, Quantum metrology of solid-state single-photon sources using photon-number-resolving detectors. New J. Phys. 21, 035007 (2019)

    Article  Google Scholar 

  32. A. Abdel-Aty, A.N. Khedr, Y.B. Saddeek, Thermal entanglement in quantum annealing processor. Int. J. Quantum Inf. 16, 1850006 (2018)

    Article  MathSciNet  Google Scholar 

  33. A. Abdel-Aty, A.N. Khedr, A.A. Youssef, Y.B. Saddeek, Entanglement of thermal state of quantum annealing processor. Thermal Sci. 24, 325 (2020)

    Article  Google Scholar 

  34. C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, Quantum coherence of the Heisenberg spin models with Dzyaloshinsky–Moriya interactions. Sci. Rep. 7, 1 (2017)

    Article  Google Scholar 

  35. A. Redwan, A. Abdel-Aty, N. Zidan, T. El-Shahat, Entanglement and teleportation of spin-chain model with multiple interactions. Chaos 29, 013138 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  36. R.F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

  37. G. Vidal, R.F. Werner, Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

  38. A. Peres, Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

  39. M. Horodecki, P. Horodecki, R. Horodecki, Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)

  40. K. Audenaert, F. Verstraete, T. De Bie, B. De Moor, Negativity and Concurrence of mixed \(2 \times 2\) states. arXiv e-prints (2000). arXiv:quant-ph/0012074v1 [quant-ph]

  41. Y. Zhang, Q. Zhou, M. Fang, G. Kang, X. Li, Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence. Quantum Inf. Process. 17, 326 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  42. D.-C. Li, Z.-L. Cao, Effect of different Dzyaloshiskii–Moriya interactions on entanglement in the Heisenberg XYZ chain. Int. J. Quantum Inf. 07(02), 547 (2009)

    Article  Google Scholar 

  43. A. Sanpera, R. Tarrach, G. Vidal, Local description of quantum inseparability. Phys. Rev. A 58, 826 (1998)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratory of High Energy and Condensed Matter Physics, Department of Physics, Faculty of Sciences Aïn Chock, University Hassan II, P.O. Box 5366, Maarif, Casablanca, 20100, Morocco

    Youssef Khedif & Abdelghani Errehymy

  2. Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco

    Mohammed Daoud

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  1. Youssef Khedif
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  2. Abdelghani Errehymy
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  3. Mohammed Daoud
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Correspondence to Youssef Khedif.

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Khedif, Y., Errehymy, A. & Daoud, M. On the thermal nonclassical correlations in a two-spin XYZ Heisenberg model with Dzyaloshinskii–Moriya interaction. Eur. Phys. J. Plus 136, 336 (2021). https://doi.org/10.1140/epjp/s13360-021-01254-w

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