Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free Public Communication

  • Go KatoEmail author
  • Masaki Owari
  • Masahito Hayashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)


Based on a secure classical network code, we propose a general method for constructing a secure quantum network code in the multiple unicast setting under restricted eavesdropper’s power. This protocol certainly transmits quantum states when there is no attack. We also show the secrecy with shared randomness as additional resource from the secrecy and the recoverability of the corresponding secure classical network code. Our protocol does not require verification process, which ensures single-shot security.


Secrecy Quantum state Network coding Multiple unicast General network 



The authors are very grateful to Professor Ning Cai and Professor Vincent Y. F. Tan for helpful discussions and comments. The works reported here were supported in part by the JSPS Grant-in-Aid for Scientific Research (A) No. 23246071, (C) No. 16K00014, (B) No. 16KT0017, (C) No. 17K05591, the Okawa Research Grant, and Kayamori Foundation of Informational Science Advancement.


  1. 1.
    Buhrman, H.R., Cleve, R., Wigderson, A.: Quantum vs. classical communication and computation. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pp. 63–68. ACM, New York (1999)Google Scholar
  2. 2.
    Raz, R.: Exponential separation of quantum and classical communication complexity. In: Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, STOC 1999, pp. 358–367. ACM, New York (1999)Google Scholar
  3. 3.
    Cai, N., Yeung, R.: Secure network coding. In: Proceedings of 2002 IEEE International Symposium on Information Theory (ISIT), p. 323 (2002)Google Scholar
  4. 4.
    Cai, N., Yeung, R.W.: Network error correction, Part 2: lower bounds. Commun. Inf. and Syst. 6(1), 37–54 (2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bhattad, K., Member, S., Narayanan, K.R.: Weakly secure network coding. In: First Workshop on Network Coding, Theory, and Applications, Riva del Garda (2005)Google Scholar
  6. 6.
    Liu, R.L.R., Liang, Y.L.Y., Poor, H., Spasojevic, P.: Secure nested codes for type II wiretap channels. In: 2007 IEEE Information Theory Workshop, pp. 337–342 (2007)Google Scholar
  7. 7.
    Rouayheb, S.Y.E., Soljanin, E.: On wiretap networks II. In: Proceedings of 2007 IEEE International Symposium on Information Theory (ISIT), pp. 551–555 (2007)Google Scholar
  8. 8.
    Harada, K., Yamamoto, H.: Strongly secure linear network coding. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E91-A(10), 2720–2728 (2008)Google Scholar
  9. 9.
    Ho, T.H.T., Leong, B.L.B., Koetter, R., Medard, M., Effros, M., Karger, D.: Byzantine modification detection in multicast networks with random network coding. IEEE Trans. Inf. Theory 54(6), 2798–2803 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jaggi, S., Langberg, M., Katti, S., Ho, T., Katabi, D., Medard, M., Effros, M.: Resilient network coding in the presence of byzantine adversaries. IEEE Trans. Inf. Theory 54(6), 2596–2603 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nutman, L., Langberg, M.: Adversarial models and resilient schemes for network coding. In: Proceedings of 2008 IEEE International Symposium on Information Theory (ISIT), pp. 171–175 (2008)Google Scholar
  12. 12.
    Yu, Z.Y.Z., Wei, Y.W.Y., Ramkumar, B., Guan, Y.G.Y.: An efficient signature-based scheme for securing network coding against pollution attacks. In: IEEE INFOCOM 2008 - The 27th Conference on Computer Communications (2008)Google Scholar
  13. 13.
    Cai, N., Chan, T.: Theory of secure network coding. Proc. IEEE 99, 421–437 (2011)CrossRefGoogle Scholar
  14. 14.
    Cai, N., Yeung, R.W.: Secure network coding on a wiretap network. IEEE Trans. Inf. Theory 57(1), 424–435 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Matsumoto, R., Hayashi, M.: Secure multiplex network coding. In: 2011 International Symposium on Networking Coding (2011).
  16. 16.
    Matsumoto, R., Hayashi, M.: Universal secure multiplex network coding with dependent and non-uniform messages. IEEE Trans. Inform. Theory; Arxiv preprint arXiv: 1111.4174 (2011) (Accepted)
  17. 17.
    Agarwal, G.K., Cardone, M., Fragouli, C.: On (secure) information flow for multiple-unicast sessions: analysis with butterfly network. arXiv: 1606.07561 (2016)
  18. 18.
    Hayashi, M., Iwama, K., Nishimura, H., Raymond, R., Yamashita, S.: Quantum network coding. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 610–621. Springer, Heidelberg (2007). CrossRefGoogle Scholar
  19. 19.
    Hayashi, M.: Prior entanglement between senders enables perfect quantum network coding with modification. Phys. Rev. A 76(4), 40301 (2007)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kobayashi, H., Le Gall, F., Nishimura, H., Rötteler, M.: General scheme for perfect quantum network coding with free classical communication. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 622–633. Springer, Heidelberg (2009). CrossRefGoogle Scholar
  21. 21.
    Leung, D., Oppenheim, J., Winter, A.: Quantum network communication; the butterfly and beyond. IEEE Trans. Inf. Theory 56(7), 3478–3490 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: Perfect quantum network communication protocol based on classical network coding. In: Proceedings of 2010 IEEE International Symposium on Information Theory (ISIT), pp. 2686–2690 (2010)Google Scholar
  23. 23.
    Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: Constructing quantum network coding schemes from classical nonlinear protocols. In: Proceedings of 2011 IEEE International Symposium on Information Theory (ISIT), pp. 109–113 (2011)Google Scholar
  24. 24.
    Chiribella, G., D’Ariano, G.M., Perinotti, P.: Quantum circuit architecture. Phys. Rev. Lett. 101, 060401 (2008)CrossRefGoogle Scholar
  25. 25.
    Chiribella, G., D’Ariano, G.M., Perinotti, P.: Theoretical framework for quantum networks. Phys. Rev. A 80, 022339 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)CrossRefGoogle Scholar
  27. 27.
    Bennett, C.H., Brassard, G., Crépeau, 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, 1895–1899 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Cheng, F., Tan, V.Y.F.: A numerical study on the wiretap network with a simple network topology. IEEE Trans. Inf. Theory 62(5), 2481–2492 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Ahlswede, R., Cai, N., Li, S.-Y.R., Yeung, R.W.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Renes, J.M.: Duality of privacy amplification against quantum adversaries and data compression with quantum side information. Proc. Roy. Soc. A 467(2130), 1604–1623 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Hayashi, M.: Quantum Information Theory: Mathematical Foundation, Graduate Texts in Physics. Springer, Heidelberg (2017). Second Edition of Quantum Information, An Introduction. Springer (2017)Google Scholar
  32. 32.
    Hayashi, M.: Group Representation for Quantum Theory. Springer, Cham (2017)CrossRefzbMATHGoogle Scholar
  33. 33.
    Hayashi, M., Owari, M., Kato, G., Cai, N.: arXiv: 1703.00723 (2017). 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 25–30 June (2017, Accepted)
  34. 34.
    Owari, M., Kato, G., Hayashi, M.: Single-shot secure quantum network coding on butterfly network with free public communication. Quantum Sci. Technol. Retrieved from arXiv:1705.01474 (2017, in Press)

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.NTT Communication Science LaboratoriesNTT CorporationTokyoJapan
  2. 2.Department of Computer Science, Faculty of InformaticsShizuoka UniversityShizuokaJapan
  3. 3.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  4. 4.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore

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