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Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction

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Abstract

We study entanglement dynamics in two-parameter qubit–qutrit states under the influence of Dzyaloshisnhkii–Moriya (DM) interaction. Our system consists of a qubit–qutrit pair as a closed system initially in two-parameter class of states, and one environmental qubit interacts with the qutrit of the closed system via DM interaction. We divide our analysis into two cases. In the first case, we study the entanglement dynamics in separable region, and in the second case we study the same in non-separable region. The DM interaction produces the entanglement in separable region with entanglement sudden death (ESD) and some states in this region remain unaffected by the same. In non-separable region, all the states are affected by DM interaction. The DM interaction excites the entanglement but does not produce ESD in this region. We observed that probability amplitude of environmental qubit does not affect the entanglement in two-parameter qubit–qutrit states in both the regions.

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References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, U.K. (2000)

    MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crépeau, 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, 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Meyer, D.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Lugiato, L.: Quantum imaging. J. Opt. B: Quantum Semiclass. 4, 3 (2002)

    Article  Google Scholar 

  7. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  8. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598–601 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Dzyaloshinsky, I.: A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. Lett. 120, 91 (1960)

    ADS  Google Scholar 

  12. Qiang, Z., Xiao-Ping, Z., Qi-Jun, Z., Zhong-Zhou, R.: Entanglement dynamics of a Heisenberg chain with Dzyaloshinskii–Moriya interaction. Chin. Phys. B 18, 3210 (2009)

    Article  ADS  Google Scholar 

  13. Qiang, Z., Ping, S., Xiao-Ping, Z., Zhong-Zhou, R.: Control of entanglement sudden death induced by Dzyaloshinskii–Moriya interaction. Chin. Phys. C 34, 1583–1586 (2010)

    Article  ADS  Google Scholar 

  14. Qiang, Z., Qi-Jun, Z., Xiao-Ping, Z., Zhong-Zhou, R.: Controllable entanglement sudden birth of Heisenberg spins. Chin. Phys. C 35, 135–138 (2011)

    Article  ADS  Google Scholar 

  15. Ann, K., Jaeger, G.: Entanglement sudden death in qubit-qutrit systems. Phys. Lett. A 372, 579–583 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Karpat, G., Gedik, Z.: Correlation dynamics of qubit-qutrit systems in a classical dephasing environment. Phys. Lett. A 375, 4166–4171 (2011)

    Article  ADS  MATH  Google Scholar 

  17. Pyo Chi, D., Lee, S.: Entanglement for a two-parameter class of states in \(2\otimes n\) quantum system. J. Phys A: Math Gen. 36, 11503–11510 (2003)

    Article  ADS  MATH  Google Scholar 

  18. YaoMin, D.I., SiPing, L.I.U., DongDong, L.I.U.: Entanglement for a two-parameter class of states in a high-dimension bipartite quantum system, Science China Physics. Mech. Astron. 53, 1868–1872 (2010)

  19. Hai-Rui, W.: Dynamics of entanglement for a two-parameter class of states in a qubit-qutrit system. Commun. Theor. Phys. 57, 983–990 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Hao, Y., Fu, W.L.: Correlation dynamics of two-parameter qubit qutrit states under decoherence. Chin. Phys. B. 22, 050303 (2013)

    Article  Google Scholar 

  21. Metwally, N.: Entangled network and quantum communication. Phys. Lett. A. 375, 4268–4273 (2011)

    Article  ADS  MATH  Google Scholar 

  22. Aty, A., Zakaria, N., Cheong, L., Metwally, N.: Effect of spin orbit interaction (Heisenberg XYZ model) on partial entangled quantum network. J Quantum Inf Sci 4, 1–17 (2014)

    Article  Google Scholar 

  23. Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit-qutrit systems under DzyaloshinskiiMoriya interaction. Quantum Inf. Process. 12, 3437–3447 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quantum Inf. Comput. 7, 1–51 (2007)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht, Netherlands (1995)

    MATH  Google Scholar 

  28. Peres, A.: Higher order Schmidt decompositions. Phys. Lett. A 202, 16–17 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Schmidt, E.: Zur theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willkrlicher funktionen nach systemen vorgeschriebener. Math. Ann. 63, 433–476 (1907)

    Article  MathSciNet  Google Scholar 

  30. Ekert, A., Knight, P.L.: Entangled quantum systems and the Schmidt decomposition. Am. J. Phys. 63, 415 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Sharma, K.K., Pandey, S.N. Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction. Quantum Inf Process 13, 2017–2038 (2014). https://doi.org/10.1007/s11128-014-0794-y

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  • DOI: https://doi.org/10.1007/s11128-014-0794-y

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