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Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions

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Abstract

The thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state are investigated. It is found that entanglement and average fidelity depend on temperature, magnetic field, and anisotropy parameter \(J_Z\). Only ferromagnetic system is suitable for quantum teleportation. \(\hbox {XZX}+\hbox {YZY}\) interaction is in favor of entanglement, average fidelity, and critical temperatures, while \(\text{ XZY }- \hbox {YZX}\) interaction against all of them. Moreover, we also find entanglement does not fully reflect average fidelity in virtue of study the relation between entanglement and average fidelity.

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References

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

    MATH  Google Scholar 

  2. Huang, Y.X., Zhan, M.S.: Properties of entanglement molecules. J. Phys. B At. Mol. Opt. Phys. 37, 3399 (2004)

    Article  ADS  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, 1899 (1993)

    Article  ADS  Google Scholar 

  4. Albert, F., Oliver, W.: Magnetic cluster excitations. Rev. Mod. Phys. 85, 367 (2013)

    Article  Google Scholar 

  5. Sørensen, A., Mølmer, K.: Spin–spin interaction and spin squeezing in an optical lattice. Phys. Rev. Lett. 83, 2277 (1999)

    Article  Google Scholar 

  6. Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 126 (1998)

    Article  ADS  Google Scholar 

  7. Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070 (1999)

    Article  ADS  Google Scholar 

  8. Vrijen, R., Yablonovitch, E., Wang, K., Jiang, H.W., Balandin, A., Roychowdhury, V., Mor, T., DiVincenzo, D.: Electron-spin-resonance transistors for quantum computing in silicon–germanium heterostructures. Phys. Rev. A 62, 12306 (2000)

    Article  ADS  Google Scholar 

  9. Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 137 (1998)

    Article  ADS  Google Scholar 

  10. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  11. Yeo, Y.: Teleportation via thermally entangled states of a two-qubit Heisenberg XX chain. Phys. Rev. A 66, 062312 (2002)

    Article  ADS  Google Scholar 

  12. Yeo, Y.: Teleportation via thermally entangled state of a two-qubit Heisenberg XX chain. Phys. Lett. A 309, 217 (2003)

    MathSciNet  ADS  Google Scholar 

  13. Hao, X., Zhu, S.Q.: Entanglement teleportation through 1D Heisenberg chain. Phys. Lett. A 338, 181 (2005)

    Article  ADS  Google Scholar 

  14. Zhou, Y., Zhang, G.F.: Quantum teleportation via a two-qubit Heisenberg XXZ chain-effects of anisotropy and magnetic field. Eur. Phys. J. D 47, 231 (2008)

    ADS  Google Scholar 

  15. Hao, J.C., Li, C.F., Guo, G.C.: Controlled dense coding using the Greenberger–Horne–Zeilinger state. Phys. Rev. A 63, 054303 (2001)

    Article  ADS  Google Scholar 

  16. Buzek, V., Hillery, M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  17. Bruss, D., DiVincenzo, D.P., Ekert, A., Fuchs, C.A., Macchiavello, C., Smolin, J.A.: Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57, 2368 (1998)

    Article  ADS  Google Scholar 

  18. Yeo, Y.: Studying the thermally entangled state of a three-qubit Heisenberg XX ring via quantum teleportation. Phys. Rev. A 68, 022316 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  19. Li, C.X., Wang, C.Z., Guo, G.C.: Entanglement and teleportation through thermal equilibrium state of spins in the XXZ model. Opt. Commun. 260, 748 (2006)

    ADS  Google Scholar 

  20. Guo, J.L., Mu, Q.X., Song, H.S.: Magnetic impurity effects on quantum teleportation via the three-qubit Heisenberg XX model. Phys. Scr. 77, 035004 (2008)

    Article  ADS  Google Scholar 

  21. Tsvelik, A.M.: Incommensurate phase of quantum one-dimensional magnetics. Phys. Rev. B 42, 779 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  22. Frahm, H.: Integrable spin-1/2 XXZ Heisenberg chain with competing interactions. J. Phys. A 25, 1417 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  23. Zvyagin, A.A.: Bethe ansatz solvable multi-chain quantum systems. J. Phys. A 34, R21 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Zvyagin, A.A., Klümper, A.: Quantum phase transitions and thermodynamics of quantum antiferromagnets with next-nearest-neighbor couplings. Phys. Rev. B 68, 144426 (2003)

    Article  ADS  Google Scholar 

  25. Lou, P., Wu, W.C., Chang, M.C.: Quantum phase transition in spin-1/2 XX Heisenberg chain with three-spin interaction. Phys. Rev. B 70, 064405 (2004)

    Article  ADS  Google Scholar 

  26. Ivanov, N., Ummethum, J., Schnack, J.: Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions. Eur. Phys. J. B 87, 10 (2014)

    Article  MathSciNet  Google Scholar 

  27. Pachos, J.K., Plenio, M.B.: Three-spin interactions in optical lattices and criticality in cluster Hamiltonians. Phys. Rev. Lett. 93, 056402 (2004)

    Article  ADS  Google Scholar 

  28. Michaud, F., Manmana, S.R., Mila, F.: Realization of higher Wess–Zumino–Witten models in spin chains. Phys. Rev. B 87, 140404(R) (2013)

    Article  ADS  Google Scholar 

  29. Michaud, F., Mila, F.: Phase diagram of the spin-1 Heisenberg model with three-site interactions on the square lattice. Phys. Rev. B 88, 094435 (2013)

    Article  ADS  Google Scholar 

  30. Wang, Z.Y., Furuya, S.C., Nakamura, M., Komakura, R.: Dimerizations in spin-S antiferromagnetic chains with three-spin interaction. Phys. Rev. B 88, 224419 (2013)

    Article  ADS  Google Scholar 

  31. Cheng, W.W., Shan, C.J., Huang, Y.X., Liu, T.K., Li, H.: Entanglement in the Heisenberg spin chain with multiple interaction. Phys. E 43, 235 (2010)

    Article  Google Scholar 

  32. Guo, J.L., Li, Z.D., Sun, Y.B.: Pairwise entanglement in the Heisenberg XX model with three-site interactions. Opt. Commun. 284, 1467 (2011)

    ADS  Google Scholar 

  33. Cheng, W.W., Shan, C.J., Sheng, Y.B., Gong, L.Y., Zhao, S.M.: Quantum correlation approach to criticality in the XX spin chain with multiple interaction. Phys. B 407, 3675 (2012)

    ADS  Google Scholar 

  34. Gottlieb, D., Rösler, J.: Exact solution of spin chain with binary and ternary interactions of Dzialoshinsky–Moriya type. Phys. Rev. B 60, 9232 (1999)

    Article  ADS  Google Scholar 

  35. Titvinidze, I., Japaridze, G.I.: Phase diagram of the spin extended model. Eur. Phys. J. B 32, 393 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. Shunsuke, C.F., Thierry, G.: Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets. Phys. Rev. B 89, 205131 (2014)

    Article  Google Scholar 

  38. Machens, A., Konstantinidis, N.P., Waldmann, O., Schneider, I., Eggert, S.: Even-odd effect in short antiferromagnetic Heisenberg chains. Phys. Rev. B 87, 144409 (2013)

    Article  ADS  Google Scholar 

  39. Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2323 (1994)

    ADS  Google Scholar 

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Acknowledgments

This project was supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 2012CB922100), the Natural Science Foundation of Hubei Province, China (Grant No. 2011CDC010 ), and the Scientific Research Foundation of the Higher Education Institutions of Hubei Province, China (Grant No. D20092204 ).

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Authors and Affiliations

  1. College of Physics and Electronic Science, Hubei Normal University, Huangshi, 435002, China

    Yu-Xing Xi & Yan-Xia Huang

  2. College of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210046, China

    Wei-Wen Cheng

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  1. Yu-Xing Xi
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  2. Wei-Wen Cheng
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  3. Yan-Xia Huang
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Correspondence to Yan-Xia Huang.

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Xi, YX., Cheng, WW. & Huang, YX. Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions. Quantum Inf Process 14, 2551–2562 (2015). https://doi.org/10.1007/s11128-015-0998-9

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  • DOI: https://doi.org/10.1007/s11128-015-0998-9

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