International Journal of Theoretical Physics

, Volume 57, Issue 2, pp 301–310 | Cite as

Entanglement Purification of Noisy Two-Qutrit States Via Environment Measurement

Article

Abstract

Entanglement swapping combined with environment measurement is proposed to purify entanglement of two-qutrit entangled states subjected to the local individual amplitude damping channels. The resultant states of our scheme have much more entanglement even though entanglement swapping itself cannot purify entanglement. When the scheme is applied to dense coding, the dense coding capacity can be significantly improved.

Keywords

Entanglement purification Environment measurement Amplitude damping Two-qutrit states 

Notes

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities under Grant No. 2015QNA44.

References

  1. 1.
    Neilsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)Google Scholar
  2. 2.
    Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)ADSCrossRefGoogle Scholar
  3. 3.
    Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., Sanpera, A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818 (1996)ADSCrossRefGoogle Scholar
  4. 4.
    Horodecki, M., Horodecki, P., Horodecki, R.: Inseparable two spin-\(\frac {1}{2}\) density matrices can be distilled to a singlet form. Phys. Rev. Lett. 78, 574 (1997)ADSCrossRefMATHGoogle Scholar
  5. 5.
    Linden, N., Massar, S., Popescu, S.: Purifying noisy entanglement requires collective measurements. Phys. Rev. Lett. 81, 3279 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    Kent, A.: Entangled mixed states and local purification. Phys. Rev. Lett. 81, 2839 (1998)ADSMathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    Duan, L.M., Giedke, G., Cirac, J.I., Zoller, P.: Entanglement purification of Gaussian continuous variable quantum states. Phys. Rev. Lett. 84, 4002 (2000)ADSCrossRefMATHGoogle Scholar
  9. 9.
    Pan, J.W., Simon, C., Brukner, C., Zeilinger, A.: Entanglement purification for quantum communication. Nature (London) 410, 1067 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 012304 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    Dür, W., Aschauer, H., Briegel, H.J.: Multiparticle entanglement purification for graph states. Phys. Rev. Lett. 91, 107903 (2003)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Pan, J.W., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature (London) 423, 417 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    Yang, M., Song, W., Cao, Z.L.: Entanglement purification for arbitrary unknown ionic states via linear optics. Phys. Rev. A 71, 012308 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    Zou, J.H., Hu, X.M.: Concentration of unknown atomic entangled states via entanglement swapping through Raman interaction. Chin. Phys. Lett 25, 3142 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Sheng, Y.B., Feng, Z.F., Ou-Yang, Y., Qu, C.C., Zhou, L.: Arbitrary partially entangled three-electron W state concentration with controlled-not gates. Chin. Phys. Lett. 31, 050303 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    Zukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: “Event-ready-detectors” bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)ADSCrossRefGoogle Scholar
  18. 18.
    Song, W., Yang, M., Cao, Z.L.: Purifying entanglement of noisy two-qubit states via entanglement swapping. Phys. Rev. A 89, 014303 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    Plama, G.M., Suominen, K.A., Ekert, A.K.: Quantum computers and dissipation. Proc. R. Soc. Lond. A 452, 567 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    Kwiat, P.G., Berglund, A.J., Alterpeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science 290, 498 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    Wang, H.F., Zhang, S., Zhu, A.D., Yi, X.X., Yeon, K.H.: Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors. Opt. Express 19, 25433 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Liu, A.P., Cheng, L.Y., Chen, L., Su, S.L., Wang, H.F., Zhang, S.: Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator. Opt. Commun. 313, 180 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    Facchi, P., Lindar, D.A., Pascazio, S.: Unification of dynamical decoupling and the quantum Zeno effect. Phys. Rev. A 69, 032314 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    Wang, S.C., Li, Y., Wang, X.B., Kwek, L.C.: Operator quantum Zeno effect: protecting quantum information with noisy two-qubit interactions. Phys. Rev. Lett. 110, 100505 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    Yao, C., Ma, Z.H., Chen, Z.H., Serafini, A.: Robust tripartite-to-bipartite entanglement localization by weak measurements and reversal. Phys. Rev. A 86, 022312 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Man, Z.X., Xia, Y.J., An, N.B.: Manipulating entanglement of two qubits in a common environment by means of weak measurements and quantum measurement reversals. Phys. Rev. A 86, 012325 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    Man, Z.X., Xia, Y.J., An, N.B.: Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements. Phys. Rev. A 86, 052322 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    Pramanik, T., Majumdar, A.S.: Improving the fidelity of teleportation through noisy channels using weak measurement. Phys. Lett. A 377, 3209 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Liao, X.P., Fang, M.F., Fang, J.S., Zhu, Q.Q.: Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement. Chin. Phys. B 23, 020304 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    Qiu, L., Tang, G., Yang, X.Q., Wang, A.M.: Enhancing teleportation fidelity by means of weak measurements or reversal. Ann. Phys. 350, 137 (2014)ADSMathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Wang, K., Zhao, X., Yu, T.: Environment-assisted quantum state restoration via weak measurements. Phys. Rev. A 89, 042320 (2014)ADSCrossRefGoogle Scholar
  33. 33.
    Xu, X.M., Cheng, L.Y., Liu, A.P., Su, S.L., Wang, H.F., Zhang, S.: Environment-assisted entanglement restoration and improvement of the fidelity for quantum teleportation. Quantum Inf. Process. 14, 4147 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Qiu, L., Liu, Z., Wang, X.: Environment-assisted entanglement purification. Quantum Inf. Comput. 16, 0982 (2016)MathSciNetGoogle Scholar
  35. 35.
    Brukner, C., Zukowski, M., Zeilinger, A.: Quantum communication complexity protocol with two entangled qutrits. Phys. Rev. Lett. 89, 197901 (2002)ADSCrossRefGoogle Scholar
  36. 36.
    Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)ADSCrossRefGoogle Scholar
  37. 37.
    Bechmann-Pasquinucci, H., Peres, A.: Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85, 3313 (2000)ADSMathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Barlett, S.D., De Guise, H., Sanders, B.C.: Quantum encodings in spin systems and harmonic oscillators. Phys. Rev. A 65, 052316 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature (London) 412, 313 (2001)ADSCrossRefGoogle Scholar
  40. 40.
    Molina-Terriza, G., Vaziri, A., Ursin, R., Zeilinger, A.: Experimental quantum coin tossing. Phys. Rev. Lett. 94, 040501 (2005)ADSCrossRefGoogle Scholar
  41. 41.
    Inoue, R., Yonehara, T., Miyamoto, Y., Koashi, M., Kozuma, M.: Measuring qutrit-qutrit entanglement of orbital angular momentum states of an atomic ensemble and a photon. Phys. Rev. Lett. 103, 110503 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    Qiu, L., Ye, B.: Thermal quantum and total correlations in spin-1 bipartite system. Chin. Phys. B 23, 050304 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    Qiu, L., Tang, G., Yang, X.Q., Xun, Z.P., Ye, B., Wang, A.M.: Sudden change of quantum discord in qutrit-qutrit system under depolarising noise. Int. J. Theor. Phys. 53, 2769 (2014)CrossRefMATHGoogle Scholar
  44. 44.
    Lanyon, B.P., Weinhold, T.J., Langford, N.K., O’Brien, J.L., Resch, K.J., Gilchrist, A., White, A.G.: Manipulating biphotonic qutrits. Phys. Rev. Lett. 100, 060504 (2008)ADSCrossRefGoogle Scholar
  45. 45.
    Walborn, S.P., Lemelle, D.S., Almeida, M.P., Souto Ribeiro, P.H.: Quantum key distribution with higher-order alphabets using spatially encoded qudits. Phys. Rev. Lett. 96, 090501 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    Nikolopoulos, G.M., Alber, G.: Security bound of two-basis quantum-key-distribution protocols using qudits. Phys. Rev. A 72, 032320 (2005)ADSCrossRefGoogle Scholar
  47. 47.
    Xiao, X., Li, Y.L.: Protecting qutrit-qutrit entanglement by weak measurement and reversal. Eur. Phys. J. D 67, 204 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    Hioe, F.T., Eberly, J.H.: N-level coherence vector and higher conservation laws in quantum optics and quantum mechanics. Phys. Rev. Lett. 47, 838 (1981)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Cheçińska, A., Wódkiewicz, K.: Separability of entangled qutrits in noisy channels. Phys. Rev. A 76, 052306 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)ADSCrossRefGoogle Scholar
  51. 51.
    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)ADSMathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    Qiu, L., Wang, A.M., Ma, X.S.: Optimal dense coding with thermal entangled states. Physica A 383, 325 (2007)ADSCrossRefGoogle Scholar
  53. 53.
    Shadman, Z., Kampermann, H., Macchiavello, C., Bruß, D.: Optimal super dense coding over noisy quantum channels. New J. Phys. 12, 073042 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    Das, T., Prabhu, R., Sen(De), A., Sen, U.: Multipartite dense coding versus quantum correlation: noise inverts relative capability of information transfer. Phys. Rev. A 90, 022319 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    Liu, B.H., Hu, X.M., Huang, Y.F., Li, C.F., Guo, G.C., Karlsson, A., Laine, E.M., Maniscalco, S., Macchiavello, C., Piilo, J.: Efficient superdense coding in the presence of non-Markovian noise. EPL 114, 10005 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Physical Science and TechnologyChina University of Mining and TechnologyXuzhouPeople’s Republic of China

Personalised recommendations