Quantum Information Processing

, Volume 14, Issue 7, pp 2599–2616 | Cite as

Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles

  • Kishore Thapliyal
  • Anirban Pathak


Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using \(n\)-qubit \((n\ge 3)\) entanglement. Specially, a large number of schemes for bidirectional controlled state teleportation are proposed using \(m\)-qubit entanglement \((m\in \{5,6,7\})\). Here, we propose a set of protocols to illustrate that it is possible to realize all these tasks related to controlled quantum communication using only Bell states and permutation of particles. As the generation and maintenance of a Bell state is much easier than a multi-partite entanglement, the proposed strategy has a clear advantage over the existing proposals. Further, it is shown that all the schemes proposed here may be viewed as applications of the concept of quantum cryptographic switch which was recently introduced by some of us. The performances of the proposed protocols as subjected to the amplitude damping and phase damping noise on the channels are also discussed.


Controlled quantum communication Bidirectional controlled teleportation Bidirectional controlled remote state preparation Quantum cryptography Quantum cryptographic switch 



AP and KT thank Department of Science and Technology (DST), India for support provided through the DST Project No. SR/S2/LOP-0012/2010.


  1. 1.
    Bennett, C.H., Brassard, G., Crï¿peau, 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)zbMATHMathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Pathak, A., Banerjee, A.: Efficient quantum circuits for perfect and controlled teleportation of \(n\)-qubit non-maximally entangled states of generalized Bell-type. Int. J. Quantum Inf. 9, 389 (2011)zbMATHCrossRefGoogle Scholar
  4. 4.
    Hillery, M., Buzek, V., Bertaiume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Wang, X.W., Xia, L.-X., Wang, Z.-Y., Zhang, D.-Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337 (2013)zbMATHMathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Huelga, S.F., Vaccaro, J.A., Chefles, A., Plenio, M.B.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63, 042303 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Huelga, S.F., Plenio, M.B., Vaccaro, J.A.: Remote control of restricted sets of operations: teleportation of angles. Phys. Rev. A 65, 042316 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    Zha, X.-W., Zou, Z.-C., Qi, J.-X., Song, H.-Y.: Bidirectional quantum controlled teleportation via five-qubit cluster state. Int. J. Theor. Phys. 52, 1740 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zha, X.-W., Song, H.-Y., Ma, G.-L.: Bidirectional swapping quantum controlled teleportation based on maximally entangled five-qubit state. quant-ph/1006.0052 (2010)Google Scholar
  12. 12.
    Li, Y.-H., Nie, L-p: Bidirectional controlled teleportation by using a five-qubit composite GHZ-Bell state. Int. J. Theor. Phys. 52, 1630 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Shukla, C., Banerjee, A., Pathak, A.: Bidirectional controlled teleportation by using 5-qubit states: a generalized view. Int. J. Theor. Phys. 52, 3790 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li, Y.-H., Li, X.-L., Sang, M.-H., Nie, Y.-Y., Wang, Z.-S.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf. Process. 12, 3835 (2013)zbMATHMathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Duan, Y.-J., Zha, X.-W.: Bidirectional quantum controlled teleportation via a six-qubit entangled state. Int. J. Theor. Phys. 53, 3780 (2014)zbMATHCrossRefGoogle Scholar
  16. 16.
    Fu, H.-Z., Tian, X.-L., Hu, Y.: A general method of selecting quantum channel for bidirectional quantum teleportation. Int. J. Theor. Phys. 53, 1840 (2014)zbMATHCrossRefGoogle Scholar
  17. 17.
    Chen, Y.: Bidirectional quantum controlled teleportation by using a genuine six-qubit entangled state. Int. J. Theor. Phys. 54, 269 (2014)Google Scholar
  18. 18.
    An, Y.: Bidirectional controlled teleportation via six-qubit cluster state. Int. J. Theor. Phys. 52, 3870 (2013)zbMATHCrossRefGoogle Scholar
  19. 19.
    Duan, Y.-J., Zha, X.-W., Sun, X.-M., Xia, J.-F.: Bidirectional quantum controlled teleportation via a maximally seven-qubit entangled state. Int. J. Theor. Phys. 53, 2697 (2014)zbMATHCrossRefGoogle Scholar
  20. 20.
    Dong, Li, Xiu, X.-M., Gao, Y.-J., Chi, F.: A controlled quantum dialogue protocol in the network using entanglement swapping. Opt. Commun. 281, 6135 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Xia, Y., Fu, C.-B., Zhang, S., Hong, S.-K., Yeon, K.-H., Um, C.-I.: Quantum dialogue by using the GHZ state. J. Korean Phys. Soc. 48, 24 (2006)Google Scholar
  22. 22.
    Hassanpour, S., Houshmand, M.: Efficient controlled quantum secure direct communication based on GHZ-like states. Quantum Inf. Process 14, 739 (2014)Google Scholar
  23. 23.
    Srinatha, N., Omkar, S., Srikanth, R., Banerjee, S., Pathak, A.: The quantum cryptographic switch. Quantum Inf. Process. 13, 59 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    Deng, F.-G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    Shukla, C., Pathak, A., Srikanth, R.: Beyond the Goldenberg–Vaidman protocol: secure and efficient quantum communication using arbitrary, orthogonal, multi-particle quantum states. Int. J. Quantum Inf. 10, 1241009 (2012)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Shukla, C., Banerjee, A., Pathak, A.: Improved protocols of secure quantum communication using W states. Int. J. Theor. Phys. 52, 1914 (2013)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Banerjee, A., Pathak, A.: Maximally efficient protocols for direct secure quantum communication. Phys. Lett. A 376, 2944 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    Yadav, P., Srikanth, R., Pathak, A.: Two-step orthogonal-state-based protocol of quantum secure direct communication with the help of order-rearrangement technique. Quantum Inf. Process. 13, 2731 (2014)zbMATHMathSciNetADSCrossRefGoogle Scholar
  29. 29.
    An, N.B.: Quantum dialogue. Phys. Lett. A 328, 6–10 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Shukla, C., Kothari, V., Banerjee, A., Pathak, A.: On the group-theoretic structure of a class of quantum dialogue protocols. Phys. Lett. A 377, 518 (2013)MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    Bennett, C. H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE international conference on computers, systems, and signal processing, Bangalore, India, p. 175 (1984)Google Scholar
  32. 32.
    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)zbMATHMathSciNetADSCrossRefGoogle Scholar
  33. 33.
    Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    Cai, Q.-Y., Li, B-w: Improving the capacity of the Boström–Felbinger protocol. Phys. Rev. A 69, 054301 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    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
  36. 36.
    Pathak, A.: Elements of Quantum Computation and Quantum Communication. CRC Press, Boca Raton (2013)zbMATHGoogle Scholar
  37. 37.
    Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New Delhi (2008)Google Scholar
  39. 39.
    Guan, X.-W., Chen, X.-B., Wang, L.-C., Yang, Y.-X.: Joint remote preparation of an arbitrary two-qubit state in noisy environments. Int. J. Theor. Phys. 53, 2236 (2014)zbMATHCrossRefGoogle Scholar
  40. 40.
    Sharma, V., Shukla, C., Banerjee, S., & Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. arXiv:1409.0833 (2014)
  41. 41.
    Srikanth, R., Banerjee, S.: Squeezed generalized amplitude damping channel. Phys. Rev. A 77, 012318 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    Macchiavello, C., Palma, G.M.: Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys. Rev. A 65, 050301 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    Cao, T.B., An, N.B.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci. Nanosci. Nanotechnol. 5, 015003 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Jaypee Institute of Information TechnologyNoidaIndia

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