Problems of Information Transmission

, Volume 40, Issue 4, pp 318–336 | Cite as

Quantum privacy and quantum wiretap channels

  • N. Cai
  • A. Winter
  • R. W. Yeung
Information Theory


Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called “quantum privacy,” Holevo quantities should be used instead of classical mutual informations. The argument actually shows that the security condition in the definition of a code should limit the wiretapper’s Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.


System Theory Mutual Information Achievable Rate Security Condition Secure Transmission 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Holevo, A.S., Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel, Probl. Peredachi Inf., 1973, vol. 9, no. 3, pp. 3–11 [Probl. Inf. Trans. (Engl. Transl.), 1973, vol. 9, no. 3, pp. 177–183].Google Scholar
  2. 2.
    von Neumann, J., Thermodynamik quantenmechanischer Gesamtheiten, Nachr. der Gesellschaft der Wiss. Gött., 1927, pp. 273–294.Google Scholar
  3. 3.
    Shannon, C.E., A Mathematical Theory of Communication, Bell Syst. Tech. J., 1948, vol. 27, no. 3, pp. 379–423; no. 4, pp. 623–656.Google Scholar
  4. 4.
    Holevo, A.S., The Capacity of a Quantum Channel with General Signal States, IEEE Trans. Inform. Theory, 1998, vol. 44, no. 1, pp. 269–273.Google Scholar
  5. 5.
    Schumacher, B. and Westmoreland, M.D., Sending Classical Information via Noisy Quantum Channels, Phys. Rev. A, 1997, vol. 56, no. 1, pp. 131–138.Google Scholar
  6. 6.
    Winter, A., Coding Theorem and Strong Converse for Quantum Channels, IEEE Trans. Inform. Theory, 1999, vol. 45, no. 7, pp. 2481–2485.Google Scholar
  7. 7.
    Holevo, A.S., Coding Theorems for Quantum Channels, LANL e-print quant-ph/9809023, 1998.Google Scholar
  8. 8.
    Schumacher, B. and Westmoreland, M.D., Relative Entropy in Quantum Information Theory, LANL e-print quant-ph/0004045, 2000.Google Scholar
  9. 9.
    Shannon, C.E., Communication Theory of Secrecy Systems, Bell Syst. Tech. J., 1949, vol. 28, no. 4, pp. 656–715.Google Scholar
  10. 10.
    Wyner, A.D., The Wire-tap Channel, Bell Syst. Tech. J., 1975, vol. 54, no. 8, pp. 1355–1387.Google Scholar
  11. 11.
    Csiszàr, I. and Körner, J., Broadcast Channels with Confidential Messages, IEEE Trans. Inform. Theory, 1978, vol. 24, no 3, pp. 339–348.Google Scholar
  12. 12.
    Ahlswede, R. and Csiszàr, I., Common Randomness in Information Theory and Crytography—Part I: Secret Sharing, IEEE Trans. Inform. Theory, 1993, vol. 39, no. 4, pp. 1121–1132.Google Scholar
  13. 13.
    Maurer, U.M., Secret Key Agreement by Public Discussion Based on Common Information, IEEE Trans. Inform. Theory, 1993, vol. 39, no. 3, pp. 733–742.Google Scholar
  14. 14.
    Cai, N. and Lam, K.Y., How to Broadcast Privacy: Secret Coding for Derministic Broadcast Channels, Numbers, Information, and Complexity, Althöfer, I., Cai, N., Dueck, G., Khachatrian, L., Pinsker, M., Sarkozy, A., Wegener, I., and Zhang, Z., Eds., Boston: Kluwer, 2000, pp. 353–368.Google Scholar
  15. 15.
    Schumacher, B. and Westmoreland, M.D., Quantum Privacy and Quantum Coherence, Phys. Rev. Lett., 1998, vol. 80, no. 25, pp. 5695–5697.Google Scholar
  16. 16.
    DiVincenzo, D.P., Shor, P.W., and Smolin, J.A., Quantum-Channel Capacity of Very Noisy Channels, Phys. Rev. A, 1998, vol. 57, no. 2, pp. 830–839.Google Scholar
  17. 17.
    Nielsen, M.A. and Chuang, I.L., Quantum Computation and Quantum Information, Cambridge: Cambridge Univ. Press, 2000.Google Scholar
  18. 18.
    Csiszàr, I. and Körner, J., Information Theory: Coding Theorems for Discrete Memoryless Systems, Budapest: Akademiai Kiado, 1981. Translated under the title Teoriya informatsii: teoremy kodirovaniya dlya diskretnykh sistem bez pamyati, Moscow: Mir, 1985.Google Scholar
  19. 19.
    Cover, T.M. and Thomas, J.A., Elements of Information Theory, New York: Wiley, 1991.Google Scholar
  20. 20.
    Yeung, R.W., A First Course in Information Theory, New York: Kluwer, 2002.Google Scholar
  21. 21.
    DiVincenzo, D.P., Horodecki, M., Leung, D.W., Smolin, J.A., and Terhal, B.M., Locking Classical Correlation in Quantum States, LANL e-print quant-ph/0303088, 2003.Google Scholar
  22. 22.
    Löber, P., Quantum Channels and Simultaneous ID Coding, Doctoral Dissertation, Bielefeld: Universität Bielefeld, 1999. Available at Scholar
  23. 23.
    Ahlswede, R. and Dueck, G., Identification via Channels, IEEE Trans. Inform. Theory, 1989, vol. 35, no. 1, pp. 15–29.Google Scholar
  24. 24.
    Ahlswede, R. and Winter, A., Strong Converse for Identification via Quantum Channels, IEEE Trans. Inf. Theory, 2002, vol. 48, no. 3, pp. 569–579. Addendum: IEEE Trans. Inf. Theory, 2003, vol. 49, no. 1, p. 346.Google Scholar
  25. 25.
    Elias, P., List Decoding for Noisy Channels, 1957 IRE Wescon Convention Record, Part 2, 1957, pp. 94–104.Google Scholar
  26. 26.
    Ahlswede, R., Channel Capacities for List Codes, J. Appl. Probab., 1973, vol. 10, no. 4, pp. 824–836.Google Scholar
  27. 27.
    Arikan, E., An Inequality on Guessing and Its Application to Sequential Decoding, IEEE Trans. Inform. Theory, 1996, vol. 42, no. 1, pp. 99–105.Google Scholar
  28. 28.
    Csiszàr, I, Almost Independence and Secrecy Capacity, Probl. Peredachi Inf., 1996, vol. 32, no. 1, pp. 48–57 [Probl. Inf. Trans. (Engl. Transl.), 1996, vol. 32, no. 1, pp. 40–47].Google Scholar
  29. 29.
    Fannes, M., A Continuity Property of the Entropy Density for Spin Lattice Systems, Comm. Math. Phys., 1973, vol. 31, pp. 291–294.Google Scholar
  30. 30.
    Devetak, I., The Private Classical Information Capacity and Quantum Information Capacity of a Quantum Channel, LANL e-print quant-ph/0304127, 2003.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2004

Authors and Affiliations

  • N. Cai
    • 1
  • A. Winter
    • 2
  • R. W. Yeung
    • 3
  1. 1.Fakultät für MathematikUniversität BielefeldGermany
  2. 2.Department of Computer ScienceUniversity of BristolUnited Kingdom
  3. 3.Department of Information EngineeringThe Chinese University of Hong KongHong Kong

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