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Entanglement concentration for concatenated Greenberger–Horne–Zeilinger state

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Abstract

The concatenated Greenberger–Horne–Zeilinger state is a new type of logic-qubit entanglement, which attracts a lot of attentions recently. In this paper, we discuss the entanglement concentration for such logic-qubit entanglement. We present two groups of entanglement concentration protocols (ECPs) for logic-qubit entanglement. In the first group, the parties do not know the initial coefficients of the partially logic-qubit entanglement. In the second group, the parties know the initial coefficients of the partially logic-qubit entanglement. In our ECPs, the unsuccessful cases can be reused to increase the total success probability in the next step. These ECPs may be useful in future long-distant quantum communication.

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References

  1. Mermin, N.D.: Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  5. 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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  8. 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)

    Article  ADS  Google Scholar 

  9. Chang, Y., Xu, C.X., Zhang, S.B., Yan, L.: Quantum secure direct communication and authentication protocol with single photons. Chin. Sci. Bull. 58, 4571 (2013)

    Article  Google Scholar 

  10. Liu, Y.: Deleting a marked state in quantum database in a duality computing mode. Chin. Sci. Bull. 58, 2927 (2013)

    Article  Google Scholar 

  11. Liu, Y., Ou-Yang, X.P.: A quantum algorithm that deletes marked states from an arbitrary database. Chin. Sci. Bull. 58, 2329 (2013)

    Article  Google Scholar 

  12. Zheng, C., Long, G.F.: Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs. Sci. Chin. Phys. Mech. Astron. 57, 1238–1243 (2014)

    Article  ADS  Google Scholar 

  13. 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)

    Article  ADS  Google Scholar 

  14. Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. Chin. Phys. Mech. Astron. 57, 1696–1702 (2014)

    Article  ADS  Google Scholar 

  15. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  16. Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194 (1999)

    Article  ADS  Google Scholar 

  17. Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)

    Article  ADS  Google Scholar 

  18. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  19. Peng, Z.H., Zou, J., Liu, X.J., Xiao, Y.J., Kuang, L.M.: Atomic and photonic entanglement concentration via photonic Faraday rotation. Phys. Rev. A 86, 034305 (2012)

    Article  ADS  Google Scholar 

  20. Shi, B.S., Jiang, Y.K., Guo, G.C.: Optimal entanglement purification via entanglement swapping. Phys. Rev. A 62, 054301 (2000)

    Article  ADS  Google Scholar 

  21. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  22. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)

    Article  ADS  Google Scholar 

  23. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  24. Du, F.F., Li, T., Ren, B.C., Wei, H.R., Deng, F.G.: Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity. J. Opt. Soc. Am. B 29, 1399–1405 (2012)

    Article  ADS  Google Scholar 

  25. Sheng, Y.B., Pan, J., Guo, R., Zhou, L., Wang, L.: Efficient N-particle W state concentration with different parity check gates. Sci. Chin. Phys. Mech. Astron. 58, 060301 (2015)

    Article  Google Scholar 

  26. Xu, T.T., Xiong, W., Ye, L.: Concentrating arbitrary four-photon less-entangled cluster state by single photons. Mod. Phys. Lett. B 26, 1250214 (2012)

    Article  ADS  Google Scholar 

  27. Li, T., Deng, F.G.: Linear-optics-based entanglement concentration of four-photon \(\chi \)-type states for quantum communication network. Int. J. Theor. Phys. 53, 3026–3034 (2014)

    Article  MATH  Google Scholar 

  28. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  29. Ren, B.C., Deng, F.G.: Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity. Laser Phys. Lett. 10, 095202 (2013)

    Article  ADS  Google Scholar 

  30. Li, X.H., Ghose, S.: Hyperentanglement concentration for time-bin and polarization hyperentangled photons. Phys. Rev. A 91, 062302 (2015)

    Article  ADS  Google Scholar 

  31. Li, X.H., Ghose, S.: Hyperconcentration for multipartite entanglement via linear optics. Laser Phys. Lett. 11, 125201 (2014)

    Article  ADS  Google Scholar 

  32. Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. Opt. Exp. 22, 6547–6561 (2014)

    Article  ADS  Google Scholar 

  33. Wang, C.: Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys. Rev. A 86, 012323 (2012)

    Article  ADS  Google Scholar 

  34. Cao, C., Wang, C., He, L.Y., Zhang, R.: Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime. Opt. Exp. 21, 4093–4105 (2013)

    Article  ADS  Google Scholar 

  35. Cao, C., Ding, H., Li, Y., Wang, T.J., Mi, S.C., Zhang, R., Wang, C.: Efficient multipartite entanglement concentration protocol for nitrogen-vacancy center and microresonator coupled systems. Quantum Inf. Process. 14, 1265–1277 (2015)

    Article  ADS  Google Scholar 

  36. Cao, C., Wang, T.J., Zhang, R., Wang, C.: Cluster state entanglement generation and concentration on nitrogen-vacancy centers in decoherence-free subspace. Laser Phys. Lett. 12, 036001 (2015)

    Article  ADS  Google Scholar 

  37. Wang, C., Cao, C., He, L.Y., Zhang, C.L.: Hybrid entanglement concentration using quantum dot and microcavity coupled system. Quantum Inf. Process. 13, 1025–1034 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Peng, Z.H., Zou, J., Liu, X.J., Kuang, L.M.: Optimal entanglement concentration via photonic Faraday rotation in cavity QED. Opt. Commun. 313, 365–368 (2014)

    Article  ADS  Google Scholar 

  39. Shukla, C., Banerjee, A.: Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states. Quantum Inf. Process. 14, 2077–2099 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  40. Wang, G.Y., Li, T., Deng, F.G.: High-efficiency atomic entanglement concentration for quantum communication network assisted by cavity QED. Quantum Inf. Process. 14, 1305–1320 (2015)

    Article  ADS  Google Scholar 

  41. Choudhury, B., Dhara, A.: An entanglement concentration protocol for cluster states. Quantum Inf. Process. 12, 2577–2585 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Du, F.F., Deng, F.G.: Heralded entanglement concentration for photon systems with linear-optical elements. Sci. Chin. Phys. Mech. Astron. 58, 40303–040303 (2015)

    Google Scholar 

  43. Zhao, J., Zheng, C.H., Shi, P., Ren, C.N., Gu, Y.J.: Generation and entanglement concentration for electron-spin entangled cluster states using charged quantum dots in optical microcavities. Opt. Commun. 322, 32–39 (2014)

    Article  ADS  Google Scholar 

  44. Zhou, L.: Consequent entanglement concentration of a less-entangled electronic cluster state with controlled-not gates. Chin. Phys. B 23, 050308 (2014)

    Article  Google Scholar 

  45. Si, B., Wen, J.J., Cheng, L.Y., Wang, H.F., Zhang, S., Yeon, K.H.: Efficient entanglement concentration schemes for separated nitrogen-vacancy centers coupled to low-Q microresonators. Int. J. Theor. Phys. 53, 80–90 (2014)

    Article  MATH  Google Scholar 

  46. Choudhury, B.S., Dhara, A.: A three-qubit state entanglement concentration protocol assisted by two-qubit systems. Int. J. Theor. Phys. 52, 3965–3969 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  47. Si, B., Su, S.L., Sun, L.L., Cheng, L.Y., Wang, H.F., Zhang, T.: Efficient three-step entanglement concentration for an arbitrary four-photon cluster state. Chin. Phys. B 22, 030305 (2013)

    Article  ADS  Google Scholar 

  48. Ji, Y.Q., Jin, Z., Zhu, A.D., Wang, H.F., Zhang, S.: Concentration of multi-photon entanglement with linear optics assisted by quantum nondemolition detection. J. Opt. Soc. Am. B 31, 994–999 (2014)

    Article  ADS  Google Scholar 

  49. Zhang, R., Zhou, S.H., Cao, C.: Efficient nonlocal two-step entanglement concentration protocol for three-level atoms in an arbitrary less-entangled W state using cavity input-output process. Sci. Chin. Phys. Mech. Astron. 57, 1511–1518 (2014)

    Article  ADS  Google Scholar 

  50. Sheng, Y.B., Liu, J., Zhao, S.Y., Zhou, L.: Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system. Chin. Sci. Bull. 59, 3507–3513 (2013)

    Article  Google Scholar 

  51. 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)

    Article  ADS  Google Scholar 

  52. Zhou, L., Sheng, Y.B., Zhao, S.M.: Optimal entanglement concentration for three-photon W states with parity check measurement. Chin. Phys. B 22, 020307 (2013)

    Article  ADS  Google Scholar 

  53. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.M.: Efficient entanglement concentration for arbitrary single-photon multimode W state. J. Opt. Soc. Am. B 30, 71–78 (2013)

    Article  ADS  Google Scholar 

  54. Zhou, L.: Efficient entanglement concentration for electron-spin W state with the charge detection. Quantum Inf. Process. 12, 2087–2101 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.M.: Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Inf. Process. 12, 1307–1320 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Fan, L.L., Xia, Y., Song, J.: Efficient entanglement concentration for arbitrary less-hyperentanglement multi-photon W states with linear optics. Quantum Inf. Process. 13, 1967–1978 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  57. Sheng, Y.B., Zhou, L.: Quantum entanglement concentration based on nonlinear optics for quantum communications. Entropy 15, 1776–1820 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  58. Fröwis, F., Dür, W.: Stable macroscopic quantum superpositions. Phys. Rev. Lett. 106, 110402 (2011)

    Article  ADS  Google Scholar 

  59. 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. Photonics 8, 364–368 (2014)

    Article  ADS  Google Scholar 

  60. Sheng, Y.B., Zhou, L.: Entanglement analysis for macroscopic Schrödinger’s Cat state. EPL 109, 40009 (2015)

    Article  ADS  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11474168 and 61401222), the Qing Lan Project in Jiangsu Province, the Natural Science Foundation of Jiangsu Province, China (Grant No. SBK2015022720) and the Priority Academic Development Program of Jiangsu Higher Education Institutions, China.

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Authors and Affiliations

  1. Institute of Signal Processing Transmission, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Chang-Cheng Qu & Yu-Bo Sheng

  2. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing, 210003, China

    Chang-Cheng Qu & Yu-Bo Sheng

  3. College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Lan Zhou

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  1. Chang-Cheng Qu
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  2. Lan Zhou
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Correspondence to Yu-Bo Sheng.

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Qu, CC., Zhou, L. & Sheng, YB. Entanglement concentration for concatenated Greenberger–Horne–Zeilinger state. Quantum Inf Process 14, 4131–4146 (2015). https://doi.org/10.1007/s11128-015-1113-y

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