Quantum Information Processing

, Volume 13, Issue 9, pp 2071–2080 | Cite as

Controlled secret sharing protocol using a quantum cloning circuit

  • Satyabrata Adhikari
  • Sovik Roy
  • Shantanav Chakraborty
  • Vinayak Jagadish
  • M. K. Haris
  • Atul Kumar
Article

Abstract

We demonstrate the possibility of controlling the success probability of a secret sharing protocol using a quantum cloning circuit. The cloning circuit is used to clone the qubits containing the encoded information and en route to the intended recipients. The success probability of the protocol depends on the cloning parameters used to clone the qubits. We also establish a relation between the concurrence of initially prepared state, entanglement of the mixed state received by the receivers after cloning scheme and the cloning parameters of cloning machine.

Keywords

Secret sharing Quantum cloning Entanglement 

References

  1. 1.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)CrossRefADSMATHGoogle Scholar
  2. 2.
    Bennett, C.H., Divincenzo, D.: Quantum information and computation. Nature 404, 247 (2000)CrossRefADSGoogle Scholar
  3. 3.
    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)MathSciNetCrossRefADSMATHGoogle Scholar
  4. 4.
    Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)CrossRefADSGoogle Scholar
  5. 5.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)CrossRefADSGoogle Scholar
  6. 6.
    Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)CrossRefADSGoogle Scholar
  8. 8.
    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)CrossRefADSGoogle Scholar
  9. 9.
    Bandyopadhyay, S.: Teleportation and secret sharing with pure entangled states. Phys. Rev. A 62, 012308 (2000)CrossRefADSGoogle Scholar
  10. 10.
    Bagherinezhad, S., Karimipour, V.: Quantum secret sharing based on reusable Greenberger–Horne–Zeilinger states as secure carriers. Phys. Rev. A 67, 044302 (2003)CrossRefADSGoogle Scholar
  11. 11.
    Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)CrossRefADSGoogle Scholar
  12. 12.
    Gordon, G., Rigolin, G.: Generalized quantum-state sharing. Phys. Rev. A 73, 062316 (2006)CrossRefADSGoogle Scholar
  13. 13.
    Zheng, S.B.: Splitting quantum information via W states. Phys. Rev. A 74, 054303 (2006)CrossRefADSGoogle Scholar
  14. 14.
    Li, Q., Chan, W.H., Long, D.-Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82, 022303 (2010)CrossRefADSGoogle Scholar
  15. 15.
    Tittel, W., Zbinden, H., Gisin, N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63, 042301 (2001)CrossRefADSGoogle Scholar
  16. 16.
    Schmidt, C., Trojek, P., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Experimental single qubit quantum secret sharing. Rev. Lett. 95, 230505 (2005)Google Scholar
  17. 17.
    Schmidt, C., Trojek, P., Gaertner, S., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Experimental quantum secret sharing. Fortschritte der Physik 54, 831 (2006)Google Scholar
  18. 18.
    Bogdanski, J., Rafiei, N., Bourennane, M.: Experimental quantum secret sharing using telecommunication fiber. Phys. Rev. A 78, 062307 (2008)Google Scholar
  19. 19.
    Buzek, V., Hillery, M.: Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers. Phys. Rev. Lett. 81, 5003 (1998)CrossRefADSGoogle Scholar
  20. 20.
    Hill, S., Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 78, 5022 (1997)Google Scholar
  21. 21.
    Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 80, 2245 (1998)Google Scholar
  22. 22.
    Bertlmann, R.A., Durstberger, K., Hiesmayr, B.C., Krammer, P.: Optimal entanglement witnesses for qubits and qutrits. Phys. Rev. A 72, 052331 (2005)CrossRefADSGoogle Scholar
  23. 23.
    Sanpera, A., Bruss, D., Lewenstein, M.: Schmidt-number witnesses and bound entanglement. Phys. Rev. A 63, 050301(R) (2001)CrossRefADSGoogle Scholar
  24. 24.
    Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)CrossRefADSGoogle Scholar
  25. 25.
    Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Satyabrata Adhikari
    • 1
  • Sovik Roy
    • 2
    • 3
  • Shantanav Chakraborty
    • 1
  • Vinayak Jagadish
    • 4
  • M. K. Haris
    • 4
  • Atul Kumar
    • 1
  1. 1.Indian Institute of TechnologyJodhpurIndia
  2. 2.Techno IndiaSalt Lake City, KolkataIndia
  3. 3.S. N. Bose National Centre for Basic SciencesSalt Lake City, KolkataIndia
  4. 4.Indian Institute of Science Education and ResearchThiruvanathapuramIndia

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