Skip to main content
SpringerLink
Log in

Pairwise quantum correlations of a three-qubit XY chain with phase decoherence

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum correlations, including entanglement and discord with its geometric measure in a three-qubit Heisenberg XY chain, with phase decoherence, are investigated when a nonuniform magnetic field is applied. When the qubits are initially in an unentangled state, the nearest neighbor pairwise correlations are destroyed by phase decoherence, but stationary correlations appear for next-to-neighbor qubits. With an inhomogeneous magnetic field, the stationary correlations appear for nearest neighbor qubits and they disappear for next-to-nearest neighbor qubits. But when the qubits are initially in an entangled state, an inhomogeneous magnetic field can enhance the stationary correlations of next-to-neighbor qubits, but it cannot do so for nearest neighbor qubits. The decoherence effect on stationary correlations is much stronger for next-to-nearest neighbor qubits than it is for nearest neighbor qubits. Finally, a uniform magnetic field can affect the correlations when the qubits are initially in an entangled state, but it cannot affect them when the qubits are initially in an unentangled state.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. Schumacher B., Westmoreland M.D.: Quantum mutual information and the one-time pad. Phys. Rev. A 74, 042305 (2006)

    Article  ADS  Google Scholar 

  3. Groisman B., Popescu S., Winter A.: Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  4. Henderson L., Vedral V.: Classical, quantum and total correlations. J. Phys. A 34, 6899–6906 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Vedral V.: Classical correlations and entanglement in quantum measurements. Phys. Rev. Lett. 90, 050401 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  6. Devetak, I., Winter, A.: Distilling common randomness from bipartite quantum states. IEEE Trans. Inf. Theory 50, 3183–3196

  7. Yang D., Horodecki M., Wang Z.D.: An additive and operational entanglement measure: conditional entanglement of mutual information. Phys. Rev. Lett. 101, 140501 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Piani M., Horodecki P., Horodecki R.: No-local-broadcasting theorem for multipartite wuantum correlations. Phys. Rev. Lett. 100, 090502 (2008)

    Article  ADS  Google Scholar 

  10. Piani M., Christandl M., Mora C.E., Horodecki P.: Broadcast copies reveal the quantumness of correlations. Phys. Rev. Lett. 102, 250503 (2009)

    Article  ADS  Google Scholar 

  11. Wang B., Xu Z.-Y., Chen Z.-Q., Feng M.: Non-Markovian effect on the quantum discord. Phys. Rev. A 81, 014101 (2010)

    Article  ADS  Google Scholar 

  12. Werlang T., Souza S., Fanchini F.F., Villas Boas C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009)

    Article  ADS  Google Scholar 

  13. Xiao X., Fang M.-F., Li Y.-L., Kang G.-D., Wu C.: Quantum discord in non-Markovian environments. Opt. Commun. 283, 3001–3005 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. 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 

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

    Article  ADS  Google Scholar 

  17. Fanchini F.F., Werlang T., Brasil C.A., Arruda L.G.E., Caldeira A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 052107 (2010)

    Article  ADS  Google Scholar 

  18. Sarandy M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  19. Eric Chitambar, http://arxiv.org/abs/1110.3057

  20. 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 

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

    Article  ADS  Google Scholar 

  22. Dakic B., Vedral V., Brukner C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

  23. Ikram M., Li F.L., Zubairy M.S.: Disentanglement in a two-qubit system subjected to dissipation environments. Phys. Rev. A 75, 062336 (2007)

    Article  ADS  Google Scholar 

  24. Guo J.L., Song H.S.: Entanglement dynamics of three-qubit coupled to an XY spin chain at finite temperature with three-site interaction. Eur. Phys. J. D 61, 791–796 (2011)

    Article  ADS  Google Scholar 

  25. Lu X.M., Xi Z.J., Sun Z., Wang X.: Geometric measure of quantum discord under decoherence. Quant. Inf. Comput. 10, 994–1003 (2010)

    MathSciNet  MATH  Google Scholar 

  26. Altintas F.: Geometric measure of quantum discord in non-Markovian environments. Opt. Commun. 283, 5264–5268 (2010)

    Article  ADS  Google Scholar 

  27. Li J.-Q., Liang J.-Q.: Quantum and classical correlations in a classical dephasing environment. Phys. Lett. A 375, 1496–1503 (2011)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. Frahm H.: Integrable spin-1/2 XXZ Heisenberg chain with competing interactions. J. Phys. A 25, 1417–1428 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  30. Zvyagin A.A.: Bethe ansatz solvable multi-chain quantum systems. J. Phys. A 34, R21–R54 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. 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 

  32. 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 

  33. Yang, M.F.: Reexamination of entanglement and the quantum phase transition. Phys. Rev. A 71, 030302-1-4 (2005)

    Google Scholar 

  34. Modi K., Paterek T., Son W., Vedral V., Williamson M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  35. Modi, K., Brodutch A., Cable H., Paterek T., Vedral V.: arXiv:1112.6238v1 [quant-ph]

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Lieb E., Schultz T., Mattis D.: Two soluble models of an antiferromagnetic chain. Ann. Phys. 16, 407–466 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. Gardiner C.W.: Quantum Noise. Springer, Berlin (1991)

    MATH  Google Scholar 

  40. Milburn G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  41. Moya-Cessa H., Buzek V., Kim M.S., Knight P.L.: Intrinsic decoherence in the atom-field interaction. Phys. Rev. A 48, 3900 (1993)

    Article  ADS  Google Scholar 

  42. Xu J.-B., Zou X.-B.: Dynamic algebraic approach to the system of a three-level atom in the Λ configuration. Phys. Rev. A 60, 4743 (1999)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Eberly J.H., Yu T.: The end of an entanglement. Science 316, 555–557 (2007)

    Article  Google Scholar 

  45. Yu T., Eberly J.H.: Sudden death of entanglement. Science 323, 598–601 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Assiut University, Assiut, Egypt

    A.-B. A. Mohamed

  2. Community College, Salman Bin Abdulaziz University, Al-Aflaj, Saudi Arabia

    A.-B. A. Mohamed

Authors
  1. A.-B. A. Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A.-B. A. Mohamed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mohamed, AB.A. Pairwise quantum correlations of a three-qubit XY chain with phase decoherence. Quantum Inf Process 12, 1141–1153 (2013). https://doi.org/10.1007/s11128-012-0460-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-012-0460-1

Keywords

Search

Navigation