Skip to main content
SpringerLink
Log in

Secure Coding for Type II Quantum Wiretap Channel

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

Abstract

This paper considers the problem of secure coding design for a type II quantum wiretap channel, where the main channel and the eavesdropper channel are both quantum channel, and the eavesdropper overhears the legitimate communication through a quantum cloning machine. Based on Calderbank-Shor-Steane (CSS)-type quantum low-density parity-check (QLDPC) codes, we show that it is possible to construct linear-time decodable codes for type II quantum wiretap channels to achieve security.

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

Similar content being viewed by others

References

  1. Wyner, A.D.: The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975)

    Article  MathSciNet  Google Scholar 

  2. Cai, N., Winter, A., Yeung, R.W.: Quantum privacy and quantum wiretap channels. Probl. Inf. Transm. 40(4), 318–336 (2004)

    Article  MathSciNet  Google Scholar 

  3. Devetak, I.: The private classical capacity and quantum capacity of a quantum channel. IEEE Trans. Inf. Theory 51(1), 44–55 (2005)

    Article  MathSciNet  Google Scholar 

  4. Renes, J.M., Renner, R.: Noisy channel coding via privacy amplification and information reconciliation. IEEE Trans. Inf. Theory 57, 7377–7385 (2011)

    Article  MathSciNet  Google Scholar 

  5. Hayashi, M.: Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information. IEEE Trans. Inf. Theory 61(10), 5595–5622 (2015)

    Article  MathSciNet  Google Scholar 

  6. Wilde, M.M.: Position-based coding and convex splitting for private communication over quantum channels. Quantum Inf. Process. 16, 264 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. Winter, A.: “Pretty strong” converse for the private capacity of degraded quantum wiretap channels. In: IEEE International Symposium on Information Theory. IEEE (2016)

  8. Anshu, A., Hayashi, M., Warsi, N.A.: Secure communication over fully quantum Gel’fand-Pinsker wiretap channel. 1801.00940 (2018)

  9. Calderbank, A.R., Rains, E.M., Shor, P.W., Solane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44(4), 1369–1387 (1998)

    Article  MathSciNet  Google Scholar 

  10. Kay, A.: Optimal universal quantum cloning: asymmetries and fidelity measure. Quantum Inf. Comput. 16, 991 (2016)

    MathSciNet  Google Scholar 

  11. Roubert, B., Braun, D.: Quantum cloning without interference. Phys. Rev. 78(04), 2311 (2008)

    Article  ADS  Google Scholar 

  12. Cernoch, A., Soubusta, J., Celechovska, L., Dusek, M., Fiurasek, J.: Experimental demonstration of optimal universal asymmetric quantum cloning of polarization states of single photons by partial symmetrization. Phys. Rev. A 80(06), 2306 (2009)

    Article  Google Scholar 

  13. Babar, Z., Botsinis, P., Alanis, D., et al.: Construction of quantum LDPC codes from classical row-circulant QC-LDPCs. IEEE Commun. Lett. 20(1), 9–12 (2016)

    Article  Google Scholar 

  14. Hagiwara, M., Imai, H.: Quantum quasi-cyclic LDPC codes. In: IEEE International Symposium on Information Theory (ISIT), pp. 806–811 (2007)

  15. Babar, Z., Botsinis, P., Alanis, D., et al.: Fifteen years of quantum LDPC coding and improved decoding strategies. IEEE Access 3, 2492–2519 (2017)

    Article  Google Scholar 

  16. Harrison, W.K., Almeida, J., Bloch, M.R., et al.: Coding for secrecy: an overview of error-control coding techniques for physical-layer security. IEEE Signal Process. Mag. 30(5), 41–50 (2013)

    Article  ADS  Google Scholar 

  17. Harrison, W.K., Almeida, J., Mclaughlin, S.W., et al.: Coding for cryptographic security enhancement using stopping sets. IEEE Trans. Inf. Forensics Secur. 6(3), 575–584 (2011)

    Article  Google Scholar 

  18. Subramanian, A., Thangaraj, A., Bloch, M., et al.: Strong secrecy on the binary erasure wiretap channel using large-girth LDPC codes. IEEE Trans. Inf. Forensics Secur. 6(3), 585–594 (2011)

    Article  Google Scholar 

  19. Orlitsky, A, Viswanathan, K, Zhang, J.: Stopping set distribution of LDPC code ensembles. IEEE Trans. Inf. Theory 51(3), 929–953 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation of China (NSFC) under grant NO. 61701375, Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JQ6063), and the Fundamental Research Funds for the central Universities (No. 300102328110).

Author information

Authors and Affiliations

  1. School of Electronic & Control Engineering, Chang’an University, Xi’an, 710064, Shaanxi, China

    Heling Xiao & Huifeng Wang

Authors
  1. Heling Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huifeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heling Xiao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, H., Wang, H. Secure Coding for Type II Quantum Wiretap Channel. Int J Theor Phys 57, 3318–3325 (2018). https://doi.org/10.1007/s10773-018-3845-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3845-9

Keywords

Search

Navigation