Generation of concatenated Greenberger–Horne–Zeilinger-type entangled coherent state based on linear optics

  • Rui Guo
  • Lan Zhou
  • Shi-Pu Gu
  • Xing-Fu Wang
  • Yu-Bo Sheng


The concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from previous protocols, each logic qubit is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.


Quantum communication Concatenated Greenberger–Horne–Zeilinger state Coherent state Linear optics 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11474168 and 61401222, the Natural Science Foundation of Jiangsu province under Grant No. BK20151502, the Qing Lan Project in Jiangsu Province, and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.


  1. 1.
    Divincenzo, D.P.: Quantum computation. Science 270, 255 (1995)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bennett, C.H., Brassard, G., Crepeau, 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 (1993)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Ekert, A.K.: Quantum cryptography based on Bell theorem. Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68, 042317 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    Hu, J.-Y., Yu, B., Jing, M.-Y., Xiao, L.-T., Jia, S.-T., Qin, G.-Q., Long, G.-L.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)CrossRefGoogle Scholar
  7. 7.
    Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell theorem. Phys. Rev. Lett. 68, 557 (1992)ADSMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Zheng, C., Long, G.F.: Quantum secure direct dialogue using Einstein–Podolsky–Rosen pairs. Sci. Chin. Phys. Mech. Astron. 57, 1238–1243 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    Cao, D.Y., Liu, B.H., Wang, Z., Huang, Y.F., Li, C.F., Guo, G.C.: Multiuser-to-multiuser entanglement distribution based on 1550 nm polarization-entangled photons. Sci. Bull. 60, 1128–1132 (2015)CrossRefGoogle Scholar
  10. 10.
    Su, X.L., Jia, X.J., Xie, C.D., Peng, K.C.: Preparation of multipartite entangled states used for quantum information networks. Sci. Chin. Phys. Mech. Astron. 57, 1210–1217 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Zhang, C., Li, C.F., Guo, G.C.: Experimental demonstration of photonic quantum ratchet. Sci. Bull. 60, 249–255 (2015)CrossRefGoogle Scholar
  12. 12.
    Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. Chin. Phys. Mech. Astron. 57, 1696–1702 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Deng, F.G., Li, C.Y., Li, Y.S., Zhou, H.Y., Wang, Y.: Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys. Rev. A 72, 022338 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein–Podolsky–Rosen pairs. Phys. Rev. A 72, 044301 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Hillery, M., Buz̆ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Pan, J.W., Chen, Z.B., Lu, C.Y., Weinfurter, H., Zeilinger, A., Zukowski, M.: Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Huang, Y.F., Liu, B.H., Peng, L., Li, Y.H., Li, L., Li, C.F., Guo, G.C.: Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state. Nat. Commun. 2, 546 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Wang, X.-L., Chen, L.-K., Li, W., Huang, H.-L., Liu, C., Chen, C., Luo, Y.-H., Su, Z.-E., Wu, D., Li, Z.-D., Lu, H., Hu, Y., Jiang, X., Peng, C.-Z., Li, L., Liu, N.L., Chen, Y.-A., Lu, C.-Y., Pan, J.-W.: Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    DiCarlo, L., Reed, M.D., Sun, L., Johnson, B.R., Chow, J.M., Gambetta, J.M., Frunzio, L., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Wei, L.F., Liu, Y.X., Nori, F.: Generation and control of Greenberger–Horne–Zeilinger entanglement in superconducting circuits. Phys. Rev. Lett. 96, 246803 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Ian, H.: Quasi-lattices of qubits for generating inequivalent multipartite entanglements. EPL 114, 50005 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Fröwis, F., Dür, W.: Stable macroscopic quantum superpositions. Phys. Rev. Lett. 106, 110402 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    Fröwis, F., Dür, W.: Stability of encoded macroscopic quantum superpositions. Phys. Rev. A 85, 052329 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    Ding, D., Yan, F.L., Gao, T.: Preparation of km-photon concatenated Greenberger–Horne–Zeilinger states for observing distinctive quantum effects at macroscopic scales. J. Opt. Soc. Am. B 30, 3075 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    Sheng, Y.B., Zhou, L.: Entanglement analysis for macroscopic Schröinger Cat state. EPL 109, 40009 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    Sheng, Y.B., Zhou, L.: Two-step complete polarization logic Bell-state analysis. Sci. Rep. 5, 13453 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    Zhou, L., Sheng, Y.B.: Complete logic Bell-state analysis assisted with photonic Faraday rotation. Phys. Rev. A 92, 042314 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Zhou, L., Sheng, Y.B.: Feasible logic Bell-state analysis with linear optics. Sci. Rep. 6, 20901 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    Zhou, L., Sheng, Y.B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)ADSCrossRefGoogle Scholar
  31. 31.
    Qu, C.C., Zhou, L., Sheng, Y.B.: Entanglement concentration for concatenated Greenberger–Horne–Zeilinger state. Quant. Inf. Process. 14, 4131–4146 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Pan, J., Zhou, L., Gu, S.P., Wang, X.F., Sheng, Y.B., Wang, Q.: Efficient entanglement concentration for concatenated Greenberger–Horne–Zeilinger state with the cross-Kerr nonlinearity. Quant. Inf. Process. 15, 1669–1687 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Lu, H., Chen, L.K., Liu, C., Xu, P., Yao, X.C., Li, L., Liu, N.L., Zhao, B., Chen, Y.A., Pan, J.W.: Experimental realization of a concatenated Greenberger–Horne–Zeilinger state for macroscopic quantum superpositions. Nat. Photon. 8, 364–368 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)ADSCrossRefMATHGoogle Scholar
  35. 35.
    Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    Zhang, Y.C., Li, Z.Y., Yu, S., Gu, W.Y., Peng, X., Guo, H.: Continuous-variable measurement-device-independent quantum key distribution using squeezed states. Phys. Rev. A 90, 052325 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    Hao, S.H., Su, X.L., Tian, C.X., Xie, C.D., Peng, K.C.: Five-wave-packet quantum error correction based on continuous-variable cluster entanglement. Sci. Rep. 5, 15462 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    Deng, X.W., Hao, S.H., Guo, H., Xie, C.D., Su, X.L.: Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators. Sci. Rep. 6, 22914 (2016)ADSCrossRefGoogle Scholar
  39. 39.
    Deng, X.W., Hao, S.H., Tian, C.X., Su, X.L., Xie, C.D., Peng, K.C.: Disappearance and revival of squeezing in quantum communication with squeezed state over a noisy channel. Appl. Phys. Lett. 108, 081105 (2016)ADSCrossRefGoogle Scholar
  40. 40.
    Su, X.L.: Applying Gaussian quantum discord to quantum key distribution. Chin. Sci. Bull. 59, 1083 (2014)CrossRefGoogle Scholar
  41. 41.
    Zhang, Y.C., Yu, S., Guo, H.: Application of practical noiseless linear amplifier in no-switching continuous-variable quantum cryptography. Quant. Inf. Process. 14, 4339–4349 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    de Faria, A.J.: Nondestructive verification of continuous-variable entanglement. Phys. Rev. A 94, 012301 (2016)ADSCrossRefGoogle Scholar
  43. 43.
    Sanders, B.C.: Entangled coherent states. Phys. Rev. A 45, 6811 (1992)ADSCrossRefGoogle Scholar
  44. 44.
    Wang, X.G.: Quantum teleportation of entangled coherent states. Phys. Rev. A 64, 022302 (2001)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Jeong, H., Kim, M.S.: Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    Jeong, H., An, N.B.: Greenberger–Horne–Zeilinger-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74, 022104 (2006)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Park, C.Y., Jeong, H.: Bell-inequality tests using asymmetric entangled coherent states in asymmetric lossy environments. Phys. Rev. A 91, 042328 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    An, N.B.: Teleportation of coherent-state superpositions within a network. Phys. Rev. A 68, 022321 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    An, N.B.: Optimal processing of quantum information via W-type entangled coherent states. Phys. Rev. A 69, 022315 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    Sheng, Y.B., Liu, J., Zhao, S.Y., Wang, L., Zhou, L.: Entanglement concentration for W-type entangled coherent states. Chin. Phys. B 23, 080305 (2014)ADSCrossRefGoogle Scholar
  51. 51.
    Sheng, Y.B., Qu, C.C., Ou-Yang, Y., Feng, Z.F., Zhou, L.: Practical entanglement concentration for entangled coherent states. Int. J. Theor. Phys. 53, 2033–2040 (2014)CrossRefMATHGoogle Scholar
  52. 52.
    Li, Z.Y., Zhang, Y.C., Wang, X.Y., Xu, B.J., Peng, X., Guo, H.: Non-Gaussian postselection and virtual photon subtraction in continuous-variable quantum key distribution. Phys. Rev. A 93, 012310 (2016)ADSCrossRefGoogle Scholar
  53. 53.
    Guo, R., Zhou, L., Gu, S.P., Wang, X.F., Sheng, Y.B.: Hybrid entanglement concentration assisted with single coherent state. Chin. Phys. B 25, 030302 (2016)CrossRefGoogle Scholar
  54. 54.
    Jeong, H., Bae, S., Choi, S.: Quantum teleportation between a single-rail single-photon qubit and a coherent-state qubit using hybrid entanglement under decoherence effects. Quant. Inf. Process. 15, 913–927 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    Wei, C.P., Hu, X.Y., Yu, Y.F., Zhang, Z.M.: Phase sensitivity of two nonlinear interferometers with inputting entangled coherent states. Chin. Phys. B 25, 040601 (2016)ADSCrossRefGoogle Scholar
  56. 56.
    Marek, P., Fiurasek, J.: Elementary gates for quantum information with superposed coherent states. Phys. Rev. A 82, 014304 (2010)ADSCrossRefGoogle Scholar
  57. 57.
    Tipsmark, A., Dong, R., Laghaout, A., Marek, P., Jezke, M., Andersen, U.L.: Experimental demonstration of a Hadamard gate for coherent state qubits. Phys. Rev. A 84, 050301 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Rui Guo
    • 1
  • Lan Zhou
    • 1
    • 2
  • Shi-Pu Gu
    • 3
  • Xing-Fu Wang
    • 2
  • Yu-Bo Sheng
    • 1
  1. 1.Key Lab of Broadband Wireless Communication and Sensor Network TechnologyNanjing University of Posts and Telecommunications, Ministry of EducationNanjingChina
  2. 2.College of Mathematics and PhysicsNanjing University of Posts and TelecommunicationsNanjingChina
  3. 3.College of Electronic Science and EngineeringNanjing University of Posts and TelecommunicationsNanjingChina

Personalised recommendations