Skip to main content
SpringerLink
Log in

Quantum Information Splitting of Arbitrary Three-Qubit State by Using Four-Qubit Cluster State and GHZ-State

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

Abstract

A scheme is proposed for quantum information splitting of arbitrary three-qubit state by using four-qubit cluster state and GHZ state as quantum channel. In the scenario, assume that the sender is called Alice, the receiver is called Bob and the controller id called Charlie. First of all, Alice performs Bell-state measurements on her qubit paris (A, 1), (B, 3), (C, 5), respectively. And then tells Charlie and Bob measure results via a classical channel. It is impossible for Bob to reconstruct the original state with local operation; if Charlie allows Bob to reconstruct the original states, he needs to perform a single particle measurement on his particle and tells Bob the results. According to the information from Alice and Charlie, Bob can reconstruct the original state with an appropriate unitary operation of his qubits 2, 4, 6.We also consider the problem of security attacks .This protocol is considered to be secure.

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

Similar content being viewed by others

References

  1. Bennett, C.H., Brassard, G.: Proc. IEEE Int. Conf. Comput. Syst. Signal Processing 175 (1984)

  2. Ekert A.K.: Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  3. Bennett, C.H., Brassard, G., Mermin, N.D.: Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Deng F.G., Long, G.L.: Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  5. Li, X.H., Deng, F.U., Zhou, H.Y.: Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  6. Li, J., Song, D.J., Guo, X.J., Jing, B.: China. Phys. C 36, 31 (2012)

    Article  ADS  MATH  Google Scholar 

  7. Huang, W., Wen, Q.Y., Jia, H.Y., Qin, S.J., Gao, F.: China. Phys. B 21, 100308 (2012)

    Article  ADS  Google Scholar 

  8. Sun, Z.W., Du, R.G., Long, D.Y.: Int. J. Theor. Phys. 51, 1946 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu, D., Chen, J.L., Jiang, W.: Int. J. Theor. Phys. 51, 2923 (2012)

    Article  MATH  Google Scholar 

  10. Ren, B.C., Wei, H.R., Hua, M., Li, T., Deng, F.G.: Eur. Phys. J. D 67, 30 (2013)

    Article  ADS  Google Scholar 

  11. Bennet, C.H., Brassard, G., Crepeau, C.: Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  12. Karlsson, A., Bourennane, M.: Phys. Rev. A 58, 4394 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  13. Gorbachev, V.N., Trubilko, A.I., Rodichkina, A.A.: Phys. Lett. A 314, 267 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. Agrawal, P., Pati, A.: Phys. Rev. A 74, 062320 (2006)

    Article  ADS  Google Scholar 

  15. Briegel, H.J., Raussendorf, R.: Phys. Rev. Lett. A 86, 910 (2001)

    Article  ADS  Google Scholar 

  16. Nie, Y.Y., Hong, Z.H., Huang, Y.B., Yi, X.J., Li, S.S.: Theor. Phys. 48, 1485 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Bouwmeester D.: Nature 390, 575–579 (1997)

    Article  ADS  Google Scholar 

  18. Walther, P., Resch, K.J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M.: Nature 434, 169–176 (2005)

  19. Karlsson, A., Kooashi, M., Imoto, N.: Phys. Rev. A 59 (1), 162–168 (1999)

    Article  ADS  Google Scholar 

  20. Zheng, S.B.: Phys. Rev. A 74 (5), 054303 (2006)

    Article  ADS  Google Scholar 

  21. Muralidharan, S., Panigrahi, P.K.: Phys. Rev. A 78, 6062333 (2008)

    Article  ADS  Google Scholar 

  22. Muralidharan, S., Panigrahi, P.K.: Opt. Commun. 284 (4), 1082–1085 (2011)

    Article  ADS  Google Scholar 

  23. Nie, Y.Y., Li, Y.H., Liu, J.C., Sang, M.H.: Quantum. Inf. Process 10 (3), 297–305 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  24. Nie, Y.Y., Li, Y.H., Liu, J.C., Sang, M.H.: Opt.Commun 284 (5), 1457–1460 (2011)

    Article  ADS  Google Scholar 

  25. Li, Y.H., Liu, J.C, Nie, Y.Y.: Int. J. Theor. Phys. 49 (10), 2592–2599 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  26. Shi, R.H., Huang, L.S., Yang, W., Zhong, H.: Int. J. Theor. Phys. 50 (11), 3329–3336 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  27. Saha, D., Panigrahi, P.K.: Quantum Inf. Process 11 (2), 615–628 (2012)

    Article  MathSciNet  Google Scholar 

  28. Nie, Y.Y., Li, Y.H., Liu, J.C., Sang, M.H.: Quantum Inf. Process 11 (2), 563–569 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. Nie, Y.Y., Li, Y.H., Liu, J.C., Sang, M.H.: Quantum Inf. Process 10, 603–608 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  30. Yin, X.F, Liu, Y.M., Zhang, W., Zhang, Z.L.: Commun. Theor. Phys. 53, 49–53 (2010)

    Article  ADS  MATH  Google Scholar 

  31. Fang, J.X., Lin, Y.S., Zhu, S.Q., Chen, X.F.: Phys. Rev. A 67, 014305 (2003)

    Article  ADS  Google Scholar 

  32. Deng, F.G., et al.: Phys. Rev. A 72, 044301 (2005)

    Article  ADS  Google Scholar 

  33. Wang, X.P., Sang, M.H.: Int. J. Theor. Phys. 53, 1064–1069 (2014)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universi-ties(ZYGX2011J064). This work is also supported partly by the National Nature Science Foundation of China under Grant (No. 60903157 and No. 61133016), and the National High Technology Joint Re-search Program of China (863 Program, Grant No. 2011AA010706).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, University of Electronic Science and Technology of China, No.2006, XiYuan Ave, West Hi-Tech Zone, Chengdu, SiChuan, 611731, People’s Republic of China

    Dong-fen Li, Rui-jin Wang & Feng-li Zhang

Authors
  1. Dong-fen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui-jin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng-li Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-fen Li.

Appendix

Appendix

Alice’s possible Bell state measurements results and the corresponding possible joint states for Bob and Charlie where the nomalization factors have been omitted for convenience.

$$\begin{array}{@{}rcl@{}} |\varPhi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle +b|0011\rangle+c|0100\rangle+d|0111\rangle+e|1000\rangle\\ &{} +f|1011\rangle-g|1100\rangle-h|1111\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle -b|0011\rangle+c|0100\rangle-d|0111\rangle+e|1000\rangle\\ &{} -f|1011\rangle-g|1100\rangle+h|1111\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle +b|0000\rangle+c|0111\rangle+d|0100\rangle+e|1011\rangle\\ &{} +f|1000\rangle-g|1111\rangle-h|1100\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle -b|0000\rangle+c|0111\rangle-d|0100\rangle+e|1011\rangle\\ &{} -f|1000\rangle+g|1111\rangle-h|1100\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle +b|0011\rangle-c|0100\rangle-d|0111\rangle+e|1000\rangle\\ &{} +f|1011\rangle+g|1100\rangle+h|1111\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle -b|0011\rangle-c|0100\rangle+d|0111\rangle+e|1000\rangle\\ &{} -f|1011\rangle+g|1100\rangle-h|1111\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle +b|0000\rangle-c|0111\rangle-d|0100\rangle+e|1011\rangle\\ &{} +f|1000\rangle+g|1111\rangle+h|1100\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle -b|0000\rangle-c|0111\rangle+d|0100\rangle+e|1011\rangle\\ &{} -f|1000\rangle+g|1111\rangle-h|1100\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle +b|0011\rangle+c|0100\rangle+d|0111\rangle-e|1000\rangle\\ &{} -f|1011\rangle+g|1100\rangle+h|1111\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle -b|0011\rangle+c|0100\rangle-d|0111\rangle-e|1000\rangle\\ &{} +f|1011\rangle+g|1100\rangle-h|1111\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle +b|0000\rangle+c|0111\rangle+d|0100\rangle-e|1011\rangle\\ &{} -f|1000\rangle+g|1111\rangle+h|1100\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle -b|0000\rangle+c|0111\rangle-d|0100\rangle-e|1011\rangle\\ &{} +f|1000\rangle+g|1111\rangle-h|1100\rangle) \end{array} $$
$$\begin{array}{@{}rcl@{}} |\varPhi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle +b|0011\rangle-c|0100\rangle-d|0111\rangle-e|1000\rangle\\ &{} -f|1011\rangle-g|1100\rangle-h|1111\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0000\rangle -b|0011\rangle-c|0100\rangle+d|0111\rangle-e|1000\rangle\\ &{} +f|1011\rangle-g|1100\rangle+h|1111\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle +b|0000\rangle-c|0111\rangle-d|0100\rangle-e|1011\rangle\\ &{} -f|1000\rangle-g|1111\rangle-h|1100\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0011\rangle -b|0000\rangle-c|0111\rangle+d|0100\rangle-e|1011\rangle\\ &{} +f|1000\rangle-g|1111\rangle+h|1100\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle+c|0000\rangle+d|0011\rangle-e|1100\rangle\\ &{} -f|1111\rangle+g|1000\rangle+h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle -b|0111\rangle+c|0000\rangle-d|0011\rangle-e|1100\rangle\\ &{} +f|1111\rangle+g|1000\rangle-h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle +b|0100\rangle+c|0011\rangle+d|0000\rangle-e|1111\rangle\\ &{} -f|1100\rangle+g|1011\rangle+h|1000\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle -b|0100\rangle+c|0011\rangle-d|0000\rangle-e|1111\rangle\\ &{} +f|1100\rangle+g|1011\rangle-h|1000\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle-c|0000\rangle-d|0011\rangle-e|1100\rangle\\ &{} -f|1111\rangle-g|1000\rangle-h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle -b|0111\rangle-c|0000\rangle+d|0011\rangle-e|1100\rangle\\ &{} +f|1111\rangle-g|1000\rangle+h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle +b|0100\rangle-c|0011\rangle-d|0000\rangle-e|1111\rangle\\ &{} -f|1100\rangle-g|1011\rangle+h|1000\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle -b|0100\rangle-c|0011\rangle-d|0000\rangle-e|1111\rangle\\ &{} +f|1100\rangle-g|1011\rangle+h|1000\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle+c|0000\rangle+d|0011\rangle+e|1100\rangle\\ &{} +f|1111\rangle-g|1000\rangle-h|1011\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle -b|0111\rangle+c|0000\rangle-d|0011\rangle+e|1100\rangle\\ &{} -f|1111\rangle-g|1000\rangle+h|1011\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle +b|0100\rangle+c|0011\rangle+d|0000\rangle+e|1111\rangle\\ &{} +f|1100\rangle-g|1011\rangle-h|1000\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle -b|0100\rangle+c|0011\rangle-d|0000\rangle+e|1111\rangle\\ &{} -f|1100\rangle-g|1011\rangle+h|1000\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle-c|0000\rangle-d|0011\rangle+e|1100\rangle\\ &{} +f|1111\rangle+g|1000\rangle+h|1011\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle -b|0111\rangle-c|0000\rangle+d|0011\rangle+e|1100\rangle\\ &{} -f|1111\rangle+g|1000\rangle-h|1011\rangle)\\ |\varPhi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle +b|0100\rangle-c|0011\rangle-d|0000\rangle+e|1111\rangle\\ &{} +f|1100\rangle+g|1011\rangle+h|1000\rangle) \end{array} $$
$$\begin{array}{@{}rcl@{}} |\varPhi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle -b|0100\rangle-c|0011\rangle+d|0000\rangle+e|1111\rangle\\ &{} -f|1100\rangle+g|1011\rangle-h|1000\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle -b|1111\rangle+c|1000\rangle+d|1011\rangle+e|0100\rangle\\ &{} +f|0111\rangle+g|0000\rangle+h|0011\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle +b|1111\rangle+c|1000\rangle-d|1011\rangle+e|0100\rangle\\ &{} -f|0111\rangle+g|0000\rangle-h|0011\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle -b|1100\rangle+c|1011\rangle+d|1000\rangle+e|0111\rangle\\ &{} +f|0100\rangle+g|0011\rangle+h|0000\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle +b|1100\rangle+c|1011\rangle-d|1000\rangle+e|0111\rangle\\ &{} -f|0100\rangle+g|0011\rangle-h|0000\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle -b|1111\rangle-c|1000\rangle-d|1011\rangle+e|0100\rangle\\ &{} +f|0111\rangle-g|0000\rangle-h|0011\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle +b|1111\rangle-c|1000\rangle+d|1011\rangle+e|0100\rangle\\ &{} -f|0111\rangle-g|0000\rangle+h|0011\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle -b|1100\rangle-c|1011\rangle-d|1000\rangle+e|0111\rangle\\ &{} +f|0100\rangle-g|0011\rangle-h|0000\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle +b|1100\rangle-c|1011\rangle+d|1000\rangle+e|0111\rangle\\ &{} -f|0100\rangle-g|0011\rangle+h|0000\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle -b|1111\rangle+c|1000\rangle+d|1011\rangle-e|0100\rangle\\ &{} -f|0111\rangle-g|0000\rangle-h|0011\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle +b|1111\rangle+c|1000\rangle-d|1011\rangle-e|0100\rangle\\ &{} +f|0111\rangle-g|0000\rangle+h|0011\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle -b|1100\rangle+c|1011\rangle+d|1000\rangle-e|0111\rangle\\ &{} -f|0100\rangle-g|0011\rangle-h|0000\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle +b|1100\rangle+c|1011\rangle-d|1000\rangle-e|0111\rangle\\ &{} +f|0100\rangle-g|0011\rangle+h|0000\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle -b|1111\rangle-c|1000\rangle-d|1011\rangle-e|0100\rangle\\ &{} -f|0111\rangle+g|0000\rangle+h|0011\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1100\rangle +b|1111\rangle-c|1000\rangle+d|1011\rangle-e|0100\rangle\\ &{} +f|0111\rangle+g|0000\rangle-h|0011\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle -b|1100\rangle-c|1011\rangle-d|1000\rangle-e|0111\rangle\\ &{} -f|0100\rangle+g|0011\rangle+h|0000\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(-a|1111\rangle +b|1100\rangle-c|1011\rangle+d|1000\rangle-e|0111\rangle\\ &{} +f|0100\rangle+g|0011\rangle-h|0000\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle +b|1011\rangle-c|1100\rangle-d|1111\rangle+e|0000\rangle\\ &{} +f|0011\rangle+g|0100\rangle+h|0111\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle -b|1011\rangle-c|1100\rangle+d|1111\rangle+e|0000\rangle\\ &{} -f|0011\rangle+g|0100\rangle-h|0111\rangle) \end{array} $$
$$\begin{array}{@{}rcl@{}} |\varPsi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle +b|1000\rangle-c|1111\rangle-d|1100\rangle+e|0011\rangle\\ &{} +f|0000\rangle+g|0111\rangle+h|0100\rangle)\\ |\varPsi^{+}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle -b|1000\rangle-c|1111\rangle+d|1100\rangle+e|0011\rangle\\ &{} -f|0000\rangle+g|0111\rangle-h|0100\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle-c|0000\rangle-d|0011\rangle-e|1100\rangle\\ &{} -f|1111\rangle-g|1000\rangle-h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle +b|0111\rangle-c|0000\rangle-d|0011\rangle-e|1100\rangle\\ &{} -f|1111\rangle-g|1000\rangle-h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|0100\rangle -b|0111\rangle-c|0000\rangle+d|0011\rangle-e|1100\rangle\\ &{} +f|1111\rangle-g|1000\rangle+h|1011\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle +b|0100\rangle-c|0011\rangle-d|0000\rangle-e|1111\rangle\\ &{} -f|1100\rangle-g|1011\rangle-h|1000\rangle)\\ |\varPhi^{+}\rangle_{A1}|\varPsi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|0111\rangle -b|0100\rangle-c|0011\rangle+d|0000\rangle-e|1111\rangle\\ &{} +f|1100\rangle-g|1011\rangle+h|1000\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle +b|1011\rangle-c|1100\rangle-d|1111\rangle-e|0000\rangle\\ &{} -f|0011\rangle-g|0100\rangle-h|0111\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle -b|1011\rangle-c|1100\rangle+d|1111\rangle-e|0000\rangle\\ &{} +f|0011\rangle-g|0100\rangle+h|0111\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle +b|1000\rangle-c|1111\rangle-d|1100\rangle-e|0011\rangle\\ &{} -f|0000\rangle-g|0111\rangle-h|0100\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{+}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle -b|1000\rangle+c|1111\rangle-d|1100\rangle-e|0011\rangle\\ &{} +f|0000\rangle-g|0111\rangle+h|0100\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{+}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle +b|1011\rangle+c|1100\rangle+d|1111\rangle-e|0000\rangle\\ &{} -f|0011\rangle+g|0100\rangle+h|0111\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPhi^{-}\rangle_{C5}=&\frac{1}{8}(a|1000\rangle -b|1011\rangle+c|1100\rangle-d|1111\rangle-e|0000\rangle\\ &{} +f|0011\rangle+g|0100\rangle-h|0111\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{+}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle +b|1000\rangle+c|1111\rangle+d|1100\rangle-e|0011\rangle\\ &{} -f|0000\rangle+g|0111\rangle+h|0100\rangle)\\ |\varPsi^{-}\rangle_{A1}|\varPhi^{-}\rangle_{B3}|\varPsi^{-}\rangle_{C5}=&\frac{1}{8}(a|1011\rangle -b|1000\rangle+c|1111\rangle-d|1100\rangle-e|0011\rangle\\ &{} +f|0000\rangle+g|0111\rangle-h|0100\rangle) \end{array} $$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Df., Wang, Rj. & Zhang, Fl. Quantum Information Splitting of Arbitrary Three-Qubit State by Using Four-Qubit Cluster State and GHZ-State. Int J Theor Phys 54, 1142–1153 (2015). https://doi.org/10.1007/s10773-014-2310-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2310-7

Keywords

Search

Navigation