Skip to main content
SpringerLink
Log in

A Strong Converse Theorem for Quantum Multiple Access Channels

  • Chapter
General Theory of Information Transfer and Combinatorics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

With the wringing technique developed by the first author for classical multiple access channels we show that the strong converse theorem holds also for quantum multiple access channels, if classical messages are transmitted.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlswede, R.: Beiträge zur Shannonschen Informationstheorie im Falle nichtstationärer Kanäle, Z. Wahrsch. und verw. Gebiete 10, 1–42 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ahlswede, R.: Multi–way communication channels. In: 2nd Intern. Symp. on Inform. Theory, Thakadsor (1971); Publ. House of the Hungarian Acad. of Sci., 23–52 (1973)

    Google Scholar 

  3. Ahlswede, R.: An elementary proof of the strong converse theorem for the multiple–access channel. J. Comb. Inform. Sys. Sci. 7, 216–230 (1982)

    MATH  MathSciNet  Google Scholar 

  4. Ahlswede, R.: Performance parameters for channels. In: Ahlswede, R., Bäumer, L., Cai, N., Aydinian, H., Blinovsky, V., Deppe, C., Mashurian, H. (eds.) General Theory of Information Transfer and Combinatorics. LNCS, vol. 4123, pp. 639–663. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Allahverdyan, A.E., Saakian, D.B.: Multi–access channels in quantum information theory (1997), http://xxx.lanl.gov/abs/quant-ph/9712034V1

  6. Arimoto, S.: On the converse to the coding theorem for discrete memoryless channels. IEEE Trans. Inform. Theory 19, 375–393 (1963)

    MathSciNet  Google Scholar 

  7. Augustin, U.: Gedächtnisfreie Kanäle für diskrete Zeit, Z. Wahrscheinlichkeitstheorie u. verw. Gebiete 6, 10–61 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dueck, G.: Maximal error capacity regions are smaller than average error capacity regions for multi–user channels. Problems of Control and Information Theory 7, 11–19 (1978)

    MATH  MathSciNet  Google Scholar 

  9. Dueck, G.: The strong converse to the coding theorem for the multiple–access channel. J. Comb. Inform. Syst. Sci. 6, 187–196 (1981)

    MATH  MathSciNet  Google Scholar 

  10. Fannes, M.: A continuity property of the entropy density for spin lattice systems. Common. Math. Phys. 31, 291–294 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fano, R.M.: Class Notes for Transmission of Information, Course 6.574. MIT, Cambridge (1952)

    Google Scholar 

  12. Feinstein, A.: A new basic theorem of information theory. IRE trans. Inform. Theory 4, 2–22 (1954)

    Article  MathSciNet  Google Scholar 

  13. Hayashi, M., Nagaoka, H.: General formulas for capacity of classical–quantum channels (2002), http://xxx.lanl.gov/abs/quant-ohy/0206186V1

  14. Holevo, A.S.: Problems in the mathematical theory of quantum communication channels. Rep. Math. Phys. 12(2), 273–278 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  15. Holevo, A.S.: The capacity of the quantum channel with general signal states. IEEE Trans. Inform Theory 44, 269–273 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Holevo, A.S.: Coding theorems for quantum channels (1998), http://xxx.lanl.giv/abs/quant–ph/9809023V1

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

    MATH  Google Scholar 

  18. Ogawa, T., Nagaoka, H.: Strong converse to the quantum channel coding theorem. IEEE Trans. Inform. Theory 45, 2486–2489 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ogawa, T., Nagaoka, H.: Strong converse and Stein’s lemma in quantum hypothesis testing. IEEE Trans. Inform. Theory 46, 2428–2433 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  20. Petz, D.: Quasientropies for states of a von Neumann algebra, vol. 21, pp. 787–800. Publ. RIMS, Kyoto Univ. (1985)

    Google Scholar 

  21. Petz, D.: Quasientropies for finite quantum systems. Rep. Math. Phys. 23, 57–65 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  22. Schumacher, B., Westmorelang, M.: Sending classical information via noisy quantum channel. Phys. Rev. A 56(1), 131–138 (1997)

    Article  Google Scholar 

  23. Shannon, C.E.: A mathematical theory of communication. Bell Sys. Tech. Journal 27, 379–423 (1948)

    MATH  MathSciNet  Google Scholar 

  24. Shannon, C.E.: Two–way communication channels. In: Proc. 4th Berkeley Symp. Math. Statist. and Prob., vol. 1, pp. 611–644. Unvi. of Calif. Press, Berkeley (1961)

    Google Scholar 

  25. Verdú, S., Han, T.S.: A general formula for channel capacity. IEEE Trans. Inform. Theory 40, 1147–1157 (1994)

    Article  MATH  Google Scholar 

  26. Winter, A.: The capacity region of the quantum multiple access channel (1998), http://xxx.lanl.gov/abs/quant–ph/9807019

  27. Winter, A.: Coding theorem and strong converse for quantum channels. IEEE Trans. Inform. Theory 45, 2481–2485 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Winter, A.: Coding theorem and strong converse for nonstationary quantum channels, Preprint 99–033, SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld (1999)

    Google Scholar 

  29. Wolfowitz, J.: The coding of message subject to chance errors. Illinois J. Math. 1, 591–606 (1957)

    MATH  MathSciNet  Google Scholar 

  30. Wolfowitz, J.: Coding Theorems of Information Theory, 3rd edn. Springer, Heidelberg (1978)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    R. Ahlswede & N. Cai

Authors
  1. R. Ahlswede
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Lars Bäumer , Ning Cai , Harout Aydinian  & Christian Deppe , ,  & 

  3. Russian Academy of Sciences Institute of Problems of Information Transmission, Bol’shoi Karetnyi per. 19, 101447, Moscow, Russia

    Vladimir Blinovsky

  4. Universität Bielefeld, Fakultät für Mathematik, Universitätsstr. 25, 33615, Bielefeld, Germany

    Haik Mashurian

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ahlswede, R., Cai, N. (2006). A Strong Converse Theorem for Quantum Multiple Access Channels. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_26

Download citation

  • DOI: https://doi.org/10.1007/11889342_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation