Skip to main content
SpringerLink
Log in

Electronic Entanglement Concentration for the Concatenated Greenberger-Horne-Zeilinger State

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, which encodes many physical qubits in a logic qubit will have important applications in both quantum communication and computation. In this paper, we will describe an entanglement concentration protocol (ECP) for electronic C-GHZ state, by exploiting the electronic polarization beam splitters (PBSs) and charge detection. This protocol has several advantages. First, the parties do not need to know the exact coefficients of the initial less-entangled C-GHZ state, which makes this protocol feasible. Second, with the help of charge detection, the distilled maximally entangled C-GHZ state can be remained for future application. Third, this protocol can be repeated to obtain a higher success probability. We hope that this protocol can be useful in future quantum computation based on electrons.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. 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  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Deng, F.G., Long, G.L., Liu, X.S.: A two-step quantum direct communication protocol using Einstein- Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)

    Article  ADS  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Zhang, C., Li, C.F., Guo, G.C.: Experimental demonstration of photonic quantum ratchet. Sci. Bull. 60, 249–255 (2015)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Fröewis, F., Düer, W.: Stable macroscopic quantum superpositions. Phys. Rev. Lett. 106, 110402 (2011)

    Article  ADS  Google Scholar 

  9. Fröwis, F., Düer, W.: Stability of encoded macroscopic quantum superpositions. Phys. Rev. A 85, 052329 (2012)

    Article  ADS  Google Scholar 

  10. Kesting, F., Fröewis, F., Düer, W.: Effective noise channels for encoded quantum systems. Phys. Rev. A 88, 042305 (2013)

    Article  ADS  Google Scholar 

  11. 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, 3075–3078 (2013)

    Article  ADS  Google Scholar 

  12. 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 

  13. Sheng, Y.B., Zhou, L.: Entanglement analysis for macroscopic Schröinger Cat state. EPL 109, 40009 (2015)

    Article  ADS  Google Scholar 

  14. Sheng, Y.B., Zhou, L.: Two-step complete polarization logic Bell-state analysis. Sci. Rep. 5, 13453 (2015)

    Article  ADS  Google Scholar 

  15. Zhou, L., Sheng, Y.B.: Complete logic Bell-state analysis assisted with photonic Faraday rotation. Phys. Rev. A 92, 042314 (2015)

    Article  ADS  Google Scholar 

  16. Zhou, L., Sheng, Y.B.: Feasible logic Bell-state analysis with linear optics. Sci. Rep. 6, 20901 (2016)

    Article  ADS  Google Scholar 

  17. Zhou, L., Sheng, Y.B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)

    Article  ADS  Google Scholar 

  18. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. 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 

  22. 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 

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

    Article  ADS  Google Scholar 

  24. 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 

  25. Du, F.F., Deng, F.G.: Heralded entanglement concentration for photon systems with linear-optical elements. Sci. China Phys. Mech. Astro. 58, 040303 (2015)

    Google Scholar 

  26. Qu, C.C., Zhou, L., Sheng, Y.B.: Entanglement concentration for concatenated Greenberger-Horne- Zeilinger state. Quantum Inf. Process. 14, 4131–4146 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. 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. Quantum Inf. Process. 15, 1669–1687 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Shukla, C., Banerjee, A., Pathak, 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  ADS  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  31. Banerjee, A., Shukla, C., Pathak, A.: Maximal entanglement concentration for a set of (n+1)-qubit states. Quantum Inf. Process. 14, 4523–4536 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Liu, H.J., Fan, L.L., Xia, Y.: Song, J.:Efficient entanglement concentration for partially entangled cluster states with weak cross-Kerr nonlinearity. Quantum Inf. Process. 14, 2909–2928 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. 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 

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

    Article  ADS  Google Scholar 

  36. 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  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. Liu, H.J., Xia, Y., Song, J.: Efficient hyperentanglement concentration for N-particle Greenberger-Horne-Zeilinger state assisted by weak cross-Kerr nonlinearity. Quantum Inf. Process. 15, 2033–2052 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Cao, C., Wang, T.J., Mi, S.C., Zhang, R., Wang, C.: Nonlocal hyperconcentration on entangled photons using photonic module system. Ann. Phys. 369, 128–138 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  41. 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 

  42. 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. Express 21, 4093–4105 (2013)

    Article  ADS  Google Scholar 

  43. Liang, B.B., Hu, S., Cui, W.X., An, C.S., Xing, Y., Hu, J.S., Sun, G.Q., Jiang, X.X., Wang, H.F.: Scheme for realizing the entanglement concentration of unknown partially entangled three-photon W states assisted by quantum dot-microcavity coupled system. Laser Phys. Lett. 11, 115202 (2014)

    Article  ADS  Google Scholar 

  44. 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 

  45. 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 

  46. 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  MATH  Google Scholar 

  47. 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 andmicroresonator coupled systems. Quantum Inf. Process. 14, 1265–1277 (2015)

    Article  ADS  MATH  Google Scholar 

  48. Sheng, Y.B., Zhou, L.: Efficient electronic entanglement concentration assisted by single mobile electrons. Chin. Phys. B 11, 110303 (2013)

    Article  Google Scholar 

  49. 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)

    Article  ADS  Google Scholar 

  50. Liu, J., Zhao, S.Y., Zhou, L., Sheng, Y.B.: Electronic cluster state entanglement concentration based on charge detection. Chin. Phys. B 23, 020313 (2014)

    Article  ADS  Google Scholar 

  51. 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 

  52. Beenakker, C.W.J., DiVincenzo, D.P., Emary, C., Kindermann, M.: Charge detection enables free-electron quantum computation. Phys. Rev. Lett. 93, 020501 (2004)

    Article  ADS  Google Scholar 

  53. Feng, X.L., Kwek, L.C., Oh, C.H.: Electronic entanglement purification scheme enhanced by charge detections. Phys. Rev. A 71, 064301 (2005)

    Article  ADS  Google Scholar 

  54. Trauzettel, B., Jordan, A.N., Beenakker, C.W.J., Büttiker, M.: Parity meter for charge qubits: an efficient quantum entangler. Phys. Rev. B 73, 235331 (2006)

    Article  ADS  Google Scholar 

  55. Zhang, X.L., Feng, M., Gao, K.L.: Cluster-state preparation and multipartite entanglement analyzer with fermions. Phys. Rev. A 73, 014301 (2006)

    Article  ADS  Google Scholar 

  56. Ionicioiu, R.: Entangling spins by measuring charge: a parity-gate toolbox. Phys. Rev. A 75, 032339 (2007)

    Article  ADS  Google Scholar 

  57. Chiu, Y.J., Chen, X., Chuang, I.L.: Fermionic Measurement-based quantum computation. Phys. Rev. A 87, 012305 (2013)

    Article  ADS  Google Scholar 

  58. Ionicioiu, R., DAmico, I.: Mesoscopic Stern-Gerlach device to polarize spin currents. Phys. Rev. B 67, 041307(R) (2003)

    Article  ADS  Google Scholar 

  59. Elzerman, J.M., Hanson, R., van Beveren, W.L.H., Vandersypen, L.M.K., Kouwenhoven, L.P.: Excited-state spectroscopy on a nearly closed quantum dot via charge detection. Appl. Phys. Lett. 84, 4617 (2004)

    Article  ADS  Google Scholar 

  60. Shaner, E.A., Lyon, S.A.: Picosecond time-resolved two-dimensional ballistic electron transport. Phys. Rev. Lett. 93, 037402 (2004)

    Article  ADS  Google Scholar 

  61. Liu, J., Zhou, L., Sheng, Y.B.: direct measurement of the concurrence for two-qubit electron spin entangled pure state based on charge detection. Chin. Phys. B 24, 070309 (2015)

    Article  ADS  Google Scholar 

  62. Matsuzaki, Y., Jefferson, J.H.: Distributed quantum information processing with mobile electrons. arXiv:1102.3121 (2011)

Download references

Acknowledgments

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

Author information

Authors and Affiliations

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

    Shang-Ping Ding & Yu-Bo Sheng

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

    Lan Zhou & Xing-Fu Wang

  3. College of Electronic Science and Engineering Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Shi-Pu Gu

Authors
  1. Shang-Ping Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shi-Pu Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xing-Fu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yu-Bo Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu-Bo Sheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, SP., Zhou, L., Gu, SP. et al. Electronic Entanglement Concentration for the Concatenated Greenberger-Horne-Zeilinger State. Int J Theor Phys 56, 1912–1928 (2017). https://doi.org/10.1007/s10773-017-3337-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-017-3337-3

Keywords

Search

Navigation