Quantum Information Processing

, Volume 12, Issue 1, pp 381–393 | Cite as

Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement

Article

Abstract

In this paper, a scheme for N-photon Greenberger–Horne–Zeilinger (GHZ) state analysis using hyperentangled states in multiple degrees of freedom with only linear optics and single photon detectors is proposed. The photons are separated and processed in different processing units. All the eight GHZ-states in either the polarization or the momentum degree of freedom can be completely distinguished. The scheme is implementable using present-day technology.

Keywords

GHZ state analyzer Hyperentanglement Complete GHZ state analyzer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nielson M.A., Chuang I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)Google Scholar
  2. 2.
    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)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Bouwmeester D., Pan J., Mattle K., Eibl M., Weinfurter H., Zeilinger A.: Experimental quantum teleportation. Nature (London) 390, 575–579 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    Boschi D., Branca S., De Martini F., Hardy L., Popescu S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121–1125 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Jennewein T., Weihs G., Pan J.-W., Zeilinger A.: Experimental nonlocality proof of quantum teleportation and entanglement swapping. Phys. Rev. Lett. 88, 017903 (2002)ADSCrossRefGoogle Scholar
  6. 6.
    de Riedmatten H., Marcikic I., van Houwelingen J.A.W., Tittel W., Zbinden H., Gisin N.: Long-distance entanglement swapping with photons from separated sources. Phys. Rev. A 71, 0500302 (2005)Google Scholar
  7. 7.
    Goebel A.M., Wagenknecht C., Zhang Q., Chen Y.-A., Chen K., Schmiedmayer J., Pan J.-W.: Multistage entanglement swapping. Phys. Rev. Lett. 101, 080403 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Mattle K., Weinfurter H., Kwiat P.G., Zeilinger A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656–4659 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    Shimizu K., Imoto N., Mukai T.: Dense coding in photonic quantum communication with enhanced information capacity. Phys. Rev. A 59, 1092–1097 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    Liu X.S., Long G.L., Tong D.M., Li F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65, 022304 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    Bennett C.H., Brassard G., Mermin N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 68, 557–559 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Ekert A.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Liu X.S., Long G.L.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Deng F.G., Long G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    Karlsson A., Bourennane M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394–4400 (1998)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Jung E., Hwang M.-R., Ju You H., Kim M.-S., Yoo S.-K., Kim H., Park D., Son J.-W., Tamaryan S., Cha S.-K.: Greenberger–Horne–Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Lu C.-Y., Yang T., Pan J.-W.: Experimental multiparticle entanglement swapping for quantum networking. Phys. Rev. Lett. 103, 020501 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    Greenberger D.M., Horne M.A., Zeilinger A.: . In: Kafatos, M. (eds) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, Kluwer, Dordrecht (1989)Google Scholar
  20. 20.
    Greenberger D.M., Horne M.A., Shimony A., Zeilinger A.: Bells theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1990)MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Wang C., Deng F.G., Li Y.S. et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    Vaindman L., Yoran N.: Methods for reliable teleportation. Phys. Rev. A 59, 116–125 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    Lütkenhaus N., Calsamiglia J., Suominen K.-A.: Bell measurements for teleportation. Phys. Rev. A 59, 3295–3300 (1999)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Calsamiglia J., Lkenhaus N.: Maximum efficiency of a linear-optical Bell-state analyzer. Appl. Phys. B: Lasers Opt. 72, 67–71 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    Calsamiglia J.: Generalized measurements by linear elements. Phys. Rev. A 65, 030301 (R) (2002)ADSCrossRefGoogle Scholar
  26. 26.
    van Houwelingen J.A.W., Brunner N., Beveratos A., Zbinden H., Gisin N.: Quantum teleportation with a three-Bell-state analyzer. Phys. Rev. Lett. 96, 130502 (2006)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Ursin R., Jennewein T., Aspelmeyer M., Kaltenbaek R., Lindenthal M., Walther P., Zeilinger A.: Communications: quantum teleportation across the Danube. Nature (London) 430, 849 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    Kwiat P.G., Weinfurter H.: Embedded Bell-state analysis. Phys. Rev. A 58, R2623–R2626 (1998)MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    Walborn S.P., Pádua S., Monken C.H.: Hyperentanglement-assisted Bell-state analysis. Phys. Rev. A 68, 042313 (2003)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    Walborn S.P., Nogueira W.A.T., Pdua S., Monken C.H.: Optical Bell-state analysis in the coincidence basis. Europhys. Lett. 62, 161 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    Ren X.-F., Guo G.-P., Guo G.-C.: Complete Bell-states analysis using hyper-entanglement. Phys. Lett. A 343, 8–11 (2005)MathSciNetADSMATHCrossRefGoogle Scholar
  32. 32.
    Barreiro J.T., Langford N.K., Peters N.A., Kwiat P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Sheng Y.B., Deng F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Sheng Y.B., Deng F.G., Long G.L.: Complete hyperentangled-Bell-state analysis for quantum communication. Phys. Rev. A 82, 032318 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    Wang C., Sheng Y.B., Deng F.G., Zhang W., Long G.L.: Efficient entanglement purification for doubly entangled photon state. Sci. China Ser. E-Tech. Sci. 52, 3464–3467 (2009)MATHCrossRefGoogle Scholar
  36. 36.
    Schuck C., Huber G., Kurtsiefer C., Weinfurter H.: Complete deterministic linear optics bell state analysis. Phys. Rev. Lett. 96, 190501 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    Barbieri M., Vallone G., Mataloni P., De Martini F.: Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement. Phys. Rev. A 75, 042317 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    Barreiro J.T., Wei Tzu-Chieh., Kwiat P.G.: Remote preparation of single-photon hybrid entangled and vector-polarization states. Phys. Rev. Lett. 105, 030407 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    Pan J.-W., Zeilinger A.: Greenberger–Horne–Zeilinger-state analyzer. Phys. Rev. A 57, 2208–2211 (1998)MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    Qian J., Feng X.-L., Gong S.-Q.: Universal Greenberger–Horne–Zeilinger-state analyzer based on two-photon polarization parity detection. Phys. Rev. A 72, 052308 (2005)ADSCrossRefGoogle Scholar
  41. 41.
    Walborn S.P., Pádua S., Monken C.H.: Hyperentanglement-assisted Bell-state analysis. Phys. Rev. A 68, 042313 (2003)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Siyu Song
    • 1
    • 2
  • Ye Cao
    • 1
    • 2
  • Yu-Bo Sheng
    • 1
    • 2
  • Gui-Lu Long
    • 1
    • 2
  1. 1.State Key Laboratory of Low-Dimensional Quantum Physics, Department of PhysicsTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Tsinghua National Laboratory for Information Science and TechnologyTsinghua UniversityBeijingPeople’s Republic of China

Personalised recommendations