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Tripartite entanglement of a spin star model with Dzialoshinski–Moriya interaction

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Abstract

The effect of Dzialoshinski–Moriya (DM) interaction on the tripartite thermal entanglement of a spin-star model with four spins has been analyzed by an entanglement measure of the tripartite negativity. Our results imply that the tripartite thermal entanglement can be established among the three surrounding parties which do not interact with each other but interact with the central party independently. From the results, we find that the strong DM interaction can enhance the tripartite thermal entanglement while the high temperature can shrink it. The effect of the inhomogeneous coupling on the tripartite thermal entanglement is also discussed.

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References

  1. Bennett C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121–3124 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Bouwmeester D., Pan J.W., Daniell M., Weinfurter H., Zeilinger A.: Observation of three-photon Greenberger-Horne-Zeilinger entanglement. Phys. Rev. Lett. 82(7), 1345–1349 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information, pp. 571–590. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  5. Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(10), 2245–2248 (1998)

    Article  ADS  Google Scholar 

  7. Zyczkowski K., Horodecki P., Sanpera A., Lewenstein M.: Volume of the set of separable states. Phys. Rev. A 58(2), 883–892 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  8. Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)

    Article  ADS  Google Scholar 

  9. Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77(8), 1413–1415 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Coffman V., Kundu J., Wootters W.K.: Distributed entanglement. Phys. Rev. A 61(5), 0532306 (2000)

    Article  ADS  Google Scholar 

  11. Yu C.S., Song H.S.: Free entanglement measure of multiparticle quantum states. Phys. Lett. A 330(5), 377–383 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Meyer D., Wallach N.R.: Global entanglement in multiparticle systems. J. Math. Phys. 43(9), 4273–4278 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Brennen G.K.: An observable measure of entanglement for pure states of multi-qubit systems. Quantum Inf. Comput. 3(6), 619–626 (2003)

    MathSciNet  MATH  Google Scholar 

  14. Pan F., Liu D., Lu G., Draayer J.P.: Simple entanglement measure for multipartite pure states. Int. J. Theor. Phys. 43(5), 1241–1247 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Facchi P., Florio G., Pascazio S.: Probability-density-function characterization of multipartite entanglement. Phys. Rev. A 74(4), 042331 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  16. Sabin C., Garcia-Alcaine G.: A classification of entanglement in three-qubit systems. Eur. Phys. J. D 48(3), 435–442 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  17. Breuer H.P., Burgarth D., Petruccione F.: Non-Markovian dynamics in a spin star system: exact solution and approximation techniques. Phys. Rev. B 70(4), 045323 (2004)

    Article  ADS  Google Scholar 

  18. Krovi H., Oreshkov O., Ryazanov M., Lidar D.A.: Non-Markovian dynamics of a qubit coupled to an Ising spin bath. Phys. Rev. A 76(5), 052117 (2007)

    Article  ADS  Google Scholar 

  19. Ferraro E., Breuer H.P., Napoli A., Jivulescu M.A., Messina A.: Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath. Phys. Rev. B 78(6), 064309 (2008)

    Article  ADS  Google Scholar 

  20. Rossini D., Facchi P., Fazio R., Florio G., Lidar D.A., Pascazio S., Plastina F., Zanardi P.: Bang-bang control of a qubit coupled to a quantum critical spin bath. Phys. Rev. A 77(5), 052112 (2008)

    Article  ADS  Google Scholar 

  21. Arshed N., Toor A.H., Lidar D.A.: Channel capacities of an exactly solvable spin-star system. Phys. Rev. A 81(6), 062353 (2010)

    Article  ADS  Google Scholar 

  22. Chen Y., Shao X.Q., Zhu A., Yeon K.H., Yu S.C.: Improving fidelity of quantum cloning via the Dzyaloshinskii–Moriya interaction in a spin network. Phys. Rev. A 81(3), 032338 (2010)

    Article  ADS  Google Scholar 

  23. Yang W.-L., Wei H., Feng M., An J.-H.: Tunable thermal entanglement in an effective spin-star system using coupled microcavities. Chinese Phys. B 18(9), 3677–3686 (2009)

    Article  ADS  Google Scholar 

  24. Anza F., Militello B., Messina A.: Tripartite thermal correlations in an inhomogeneous spinCstar system. J. Phys. B 43(20), 205501 (2010)

    Article  ADS  Google Scholar 

  25. Militello B., Messina A.: Genuine tripartite entanglement in a spin-star network at thermal equilibrium. Phys. Rev. A 83(4), 042305 (2011)

    Article  ADS  Google Scholar 

  26. Huber M., Mintert F., Gabriel A., Hiesmayr B.C.: Detection of high-dimensional genuine multipartite entanglement of mixed states. Phys. Rev. Lett. 104(21), 210501 (2010)

    Article  ADS  Google Scholar 

  27. Dzialoshinski I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solid 4(4), 241–255 (1958)

    Article  ADS  Google Scholar 

  28. Moriya T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4(5), 228–230 (1960)

    Article  ADS  Google Scholar 

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Correspondence to Xiao San Ma.

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Ma, X.S., Zhao, G.X., Zhang, J.Y. et al. Tripartite entanglement of a spin star model with Dzialoshinski–Moriya interaction. Quantum Inf Process 12, 321–329 (2013). https://doi.org/10.1007/s11128-012-0378-7

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  • DOI: https://doi.org/10.1007/s11128-012-0378-7

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