Skip to main content
Log in

Controlled probabilistic quantum key distribution using a ground state

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose two controlled probabilistic quantum key distribution protocols with AKLT states. An AKLT state is a gapped ground state with minimum energy, and owing to the properties of this special state, our proposed protocols incorporate not only the measurement uncertainty in quantum phenomena (entanglement swapping with 1/4 probability) but also additional randomness (Bell measurement on two physical particles with 1/3 probability), in comparison with other PQKD schemes. Therefore, our protocols are more suitable for use by two mutually untrusted communicants, with no authenticated intermediate channel, allowing them to obtain an unpredictable, and therefore secure, key.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing (invited paper). In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pp. 175–179 (1984)

  2. Bennett, C.H.: Quantum cryptography using any two non-orthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. Bruss, D.: Optimal eavesdropping in quantum cryptography with six states. Phys. Rev. Lett. 81(14), 3018–3021 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. Gan, G.: Quantum key distribution scheme with high efficiency. Commun. Theor. Phys. 51(5), 820–822 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Li, C., Song, H.S., Zhou, L., Wu, C.F.: A random quantum key distribution achieved by using Bell states. J. Opt. B Quantum Semiclass. Opt. 5(2), 155–157 (2003)

    Article  ADS  Google Scholar 

  8. Song, D.: Secure key distribution by swapping quantum entanglement. Phys. Rev. A 69(3), 034301 (2004)

    Article  ADS  Google Scholar 

  9. Ma, X.F., Qi, B., Zhao, Y., Lo, H.K.: Practical decoy state for quantum key distribution (2005). arXiv:quant-ph/0503005v5

  10. 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 

  11. Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  12. Biham, E., Boyer, M., Boykin, P.O., Mor, T., Roychowdhury, V.: A proof of the security of quantum key distribution. In: Proceedings of the Thirty-second Annual ACM Symposium on Theory of Computing, Portland, Oregon, USA, pp. 715–724 (2000)

  13. Gottesman, D., Lo, H.K.: Proof of security of quantum key distribution with two-way classical communications. IEEE Trans. Inf. Theory 49(2), 457–475 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lo, H.K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999)

    Article  ADS  Google Scholar 

  15. Mayers, D.: Unconditional security in quantum cryptography. J. ACM 48, 351–406 (2001)

    Article  MathSciNet  Google Scholar 

  16. Lo, H.K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005)

    Article  ADS  Google Scholar 

  17. Ben-Or, M., Horodecki, M., Leung, D.W., Mayers, D., Oppenheim, J.: The universal composable security of quantum key distribution. In: Proceedings of the 2nd Theory of Cryptography Conference, Lecture Notes in Computer Science/Security and Cryptology, vol. 3378, Cambridge, MA, USA, pp. 386–406 (2005)

  18. Hwang, T., Tsai, C.-W., Chong, S.-K.: Probabilistic quantum key distribution. Quantum Inf. Comput. 11(7–8), 615–637 (2011)

    MATH  MathSciNet  Google Scholar 

  19. Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283(6), 1192–1195 (2010)

    Article  ADS  Google Scholar 

  20. Chong, S.K., Tsai, C.W., Hwang, T.: Improvement on “quantum key agreement protocol with maximally entangled states”. Int. J. Theor. Phys. 50(6), 1793–1802 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hsueh, C.C., Chen, C.Y.: Quantum key agreement protocol with maximally entangled states. In: Proceedings of the 14th Information Security Conference (ISC 2004), National Taiwan University of Science and Technology, Taipei, Taiwan, pp. 236–242 (2004)

  22. Tsai, C.W., Chong, S.K., Hwang, T.: Comment on quantum key agreement protocol with maximally entangled states. In: Proceedings of the 20th Cryptology and Information Security Conference (CISC 2010), National Chiao Tung University, Hsinchu, Taiwan, pp. 210–213 (2010)

  23. Tsai, C.W., Hwang, T.: On “quantum key agreement protocol”. Technical Report, C-S-I-E, NCKU. R.O.C, Taiwan (2009)

  24. Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40(18), 1149–1150 (2004)

    Article  Google Scholar 

  25. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Valence bond ground states in isotropic quantum antiferromagnets. Commun. Math. Phys. 115, 477–528 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  26. Liu, L.L., Hwang, T.: Controlled remote state preparation protocols via AKLT states. Quantum Inf. Process (2014). doi:10.1007/s11128-014-0757-3

    MathSciNet  Google Scholar 

  27. Chen, X., Zeng, B., Gu, Z.C., Yoshida, B., Chuang, I.L.: Gapped two-body Hamiltonian whose unique ground state is universal for one-way quantum computation. Phys. Rev. Lett. 102, 220501 (2009)

    Article  ADS  Google Scholar 

  28. Kempe, J., Bacon, D., Lidar, D.A., Whaley, K.B.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2001)

    Article  ADS  Google Scholar 

  29. Nguyen, B.A.: Joint remote state preparation via W and W-type states. Opt. Commun. 283, 4113–4117 (2010)

    Article  Google Scholar 

  30. Darmawan, A.S., Bartlett, S.D.: Optical spin-1 chain and its use as a quantum-computational wire. Phys. Rev. A 82, 012328 (2010)

    Article  ADS  Google Scholar 

  31. Kaltenbaek, R., Lavoie, J., Zeng, B., Bartlett, S.D., Resch, K.J.: Optical one-way quantum computing with a simulated valence-bond solid. Nat. Phys. let. 6, 850–854 (2010)

    Article  Google Scholar 

  32. Coello, J.G., Bayat, A., Bose, S., Jefferson, J.H., Creffield, C.E.: Spin filtering and entanglement swapping through coherent evolution of a single quantum dot. Phys. Rev. Lett. 105, 080502 (2010)

    Article  ADS  Google Scholar 

  33. Fan, H., Korepin, V., Roychowdhury, V.: Entanglement in a valence-bond solid state. Phys. Rev. Lett. 93, 227203 (2004)

    Article  ADS  Google Scholar 

  34. Gao, F., Lin, S., Wen, Q.Y., Zhu, F.C.: A special eavesdropping on one-sender versus n-receiver QSDC protocol. Chin. Phys. Lett. 25(5), 1561–1563 (2008)

    Article  ADS  Google Scholar 

  35. Qin, S.J., Wen, Q.Y., Meng, L.M., Zhu, F.C.: Comment on “Controlled DSQC using five-qubit entangled states and two-step security test”. Opt. Commun. 282(13), 2656–2658 (2009)

    Article  ADS  Google Scholar 

  36. Gao, G., Qin, S.J., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger state. Opt. Commun. 283(1), 192–195 (2010)

    Article  ADS  Google Scholar 

  37. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tzonelih Hwang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, LL., Hwang, T. Controlled probabilistic quantum key distribution using a ground state. Quantum Inf Process 14, 989–1003 (2015). https://doi.org/10.1007/s11128-014-0901-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0901-0

Keywords

Navigation