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Measurement-induced disturbance and negativity in mixed-spin XXZ model

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Abstract

In this paper, we investigate the quantum phase transition (QTP) and quantum correlation in the one-dimensional mixed-spin (1/2, 1) XXZ model with Dzyaloshinskii–Moriya (DM) interaction under an inhomogeneous magnetic field. By controlling the strength of DM interaction and inhomogeneous magnetic field, we can change the phase transition points. The results show that the DM interaction plays an important role in improving the quantum correlation, which can be gained at higher temperature by choosing the proper strength of DM interaction. Moreover, the homogeneous magnetic field cannot change the critical temperature \(T_{c}\) alone, while the inhomogeneous magnetic parameter \(b\) can suppress the effects of temperature on negativity. In addition, we make an explicit comparison between the negativity and measurement-induced disturbance (MID) for this model and discover that MID is more robust than thermal entanglement against temperature \(T\) and may reveal more properties about quantum correlations of the system than entanglement. Furthermore, in some circumstances, the MID can detect the critical points of quantum phase transition while the negativity cannot.

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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 Communication. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  3. Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392–2395 (2000)

    Article  ADS  Google Scholar 

  4. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature (London) 404, 247–255 (2000)

    Article  ADS  Google Scholar 

  5. Kim, Y.H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete bell state measurement. Phys. Rev. Lett. 86, 1370–1373 (2001)

    Article  ADS  Google Scholar 

  6. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Song, X.K., Wu, T., Ye, L.: Negativity and quantum phase transition in the anisotropic XXZ model. Eur. Phys. J. D 67, 96 (2013)

    Article  ADS  Google Scholar 

  8. Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transitions. Nature (London) 416, 608–610 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  12. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  13. Dakic, B., et al.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

  14. Chen, Y.X., Li, S.W., Yin, Z.: Quantum correlations in a clusterlike system. Phys. Rev. A 82, 052320 (2010)

    Article  ADS  Google Scholar 

  15. Hassan, A., Lari, B., Joag, P.: Thermal quantum and classical correlations in a two-qubit XX model in a nonuniform external magnetic field. J. Phys. A Math. Theory 43, 485302 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  16. Hao, X., Ma, C.L., Sha, J.Q.: Decoherence of quantum discord in an asymmetric-anisotropy spin system. J. Phys. A Math. Theory 43, 425302 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  17. Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  18. Chang, L., Luo, S.: Remedying the local ancilla problem with geometric discord. Phys. Rev. A 87, 062303 (2013)

    Article  ADS  Google Scholar 

  19. Sun, Z., Lu, X.M., Song, L.J.: Quantum discord induced by a spin chain with quantum phase transition. J. Phys. B At. Mol. Opt. Phys. 43, 215504 (2010)

    Article  ADS  Google Scholar 

  20. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  21. Amesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)

    Article  ADS  Google Scholar 

  22. Wang, X.G.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. A 64, 012313 (2001)

    Article  ADS  Google Scholar 

  23. Zhou, L., Song, H.S., Guo, Y.Q., Li, C.: Enhanced thermal entanglement in an anisotropic Heisenberg XYZ chain. Phys. Rev. A 68, 024301 (2003)

    Article  ADS  Google Scholar 

  24. Zhang, G.F., Li, S.S.: Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field. Phys. Rev. A 72, 034302 (2005)

    Article  ADS  Google Scholar 

  25. Guo, J.L., Song, H.S.: Entanglement and teleportation through a two-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya interaction. Eur. Phys. J. D 56, 265–269 (2010)

    Article  ADS  Google Scholar 

  26. Tufarelli, T., Girolami, D., Vasile, R., Bose, S., Adesso, G.: Quantum resources for hybrid communication via qubit-oscillator states. Phys. Rev. A 86, 052326 (2012)

    Article  ADS  Google Scholar 

  27. Yao, Y., et al.: Quantum discord in quantum random access codes and its connection with dimension witness. Phys. Rev. A 86, 062310 (2012)

    Article  ADS  Google Scholar 

  28. Xu, S., Song, X.K., Ye, L.: Negativity and geometric quantum discord as indicators of quantum phase transition in the XY model with Dzyaloshinskii-Moriya interaction. Int. J. Mod. Phys. B. 27, 1350074 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  29. Yao, Y., et al.: Performance of various correlation measures in quantum phase transitions using the quantum renormalization-group method. Phys. Rev. A 86, 042102 (2012)

    Article  ADS  Google Scholar 

  30. Ma, F.W., Liu, S.X., Kong, X.M.: Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii–Moriya interaction. Phys. Rev. A 84, 042302 (2011)

    Article  ADS  Google Scholar 

  31. Werlang, T., Rigolin, G.: Thermal and magnetic quantum discord in Heisenberg models. Phys. Rev. A 81, 044101 (2010)

    Article  ADS  Google Scholar 

  32. Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)

    Article  ADS  Google Scholar 

  33. Guo, J.L., Mi, Y.J., Zhang, J., Song, H.S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504 (2011)

    Article  ADS  Google Scholar 

  34. Zhang, G.F., Fan, H., Li, A.L., Jiang, Z.T., Abliz, A., Liu, W.M.: Quantum correlations in spin models. Ann. Phys. 326, 2694–2701 (2011)

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. Miranowicz, A., Grudka, A.: A comparative study of relative entropy of entanglement, concurrence and negativity. J. Opt. B Quantum Semiclass. Opt. 6, 542–548 (2004)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China under Grants Nos. 11074002 and 61275119, the Doctoral Foundation of the Ministry of Education of China under Grant No. 20103401110003, and also by the Personal Development Foundation of Anhui Province (2008Z018).

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  1. School of Physics and Material Science, Anhui University, Hefei, 230039, People’s Republic of China

    Shuai Xu, Xue-ke Song & Liu Ye

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  1. Shuai Xu
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  2. Xue-ke Song
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  3. Liu Ye
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Correspondence to Liu Ye.

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Xu, S., Song, Xk. & Ye, L. Measurement-induced disturbance and negativity in mixed-spin XXZ model. Quantum Inf Process 13, 1013–1024 (2014). https://doi.org/10.1007/s11128-013-0706-6

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  • DOI: https://doi.org/10.1007/s11128-013-0706-6

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