Skip to main content
SpringerLink
Log in

Simplification of Additivity Conjecture in Quantum Information Theory

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. In this paper, by using some unital extension of quantum channels, we show that proving one of these conjectures for all unital quantum channels would imply that it is also true for all quantum channels.

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.

Similar content being viewed by others

References

  1. R. Alicki and M. Fannes, “Note on multiple additivity of minimal Renyi entropy output of the Werner-Holevo channels”, quant-ph/0407033.

  2. G. G. Amosov, Remark on the additivity conjecture for the quantum depolarizing channel, quant-ph/0408004.

  3. K. M. R. Audenaert and S. L. Braunstein, Comm. Math. Phys. 246 443 (2004), quant-ph/0303045.

    Google Scholar 

  4. N. Datta, A. S. Holevo, and Y. Suhov, A quantum channel with additive minimum output entropy, quant-ph/0403072.

  5. N. Datta, A. S. Holevo, and Y. Suhov, Additivity for transpose depolarizing channels, quant-ph/0412034.

  6. N. Datta and M. B. Ruskai, J. Phys. A, 38 9785, (2005), quant-ph/0505048.

  7. M. Fannes, B. Haegeman, M. Mosonyi, and D. Vanpeteghem, Additivity of minimal entropy output for a class of covariant channels, quant-ph/0410195.

  8. A. Fujiwara and T. Hashizumé, Phys. lett. A, 299 469 (2002).

    Google Scholar 

  9. M. Fukuda, J. Phys. A, 38 L753 (2005), quant-ph/0505022.

  10. A. S. Holevo, Remarks on the classical capacity of quantum channel, quant-ph/0212025.

  11. King C. (2002) J. Math. Phys. 43: 4641

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. C. King, Maximal p-norms of entanglement breaking channels, quant-ph/0212057.

  13. King C. (2003) IEEE Trans. Inform. Theory 49: 221

    Article  MATH  MathSciNet  Google Scholar 

  14. C. King, An application of a matrix inequality in quantum information theory, quant-ph/0412046.

  15. C. King and M. B. Ruskai, IEEE Trans. Info. Theory, 47 192 (2001), quant-ph/9911079.

    Google Scholar 

  16. Matsumoto K, Shimono T., Winter A. (2004) Comm. Math. Phys. 246(3): 427

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Matsumoto K., Yura F. (2004) J. Phys. A, 37: L167

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. A. A. Pomeransky, Phys. Rev. A, 68 032317 (2003), quant-ph/0305056.

    Google Scholar 

  19. Shor P.W. (2002) J. Math. Phys. 43: 4334

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. P. W. Shor, Comm. Math. Phys. 246(3) 453 (2004), quant-ph/0305035.

    Google Scholar 

  21. R. F. Werner and A. S. Holevo, J. Math. Phys. 43 4353 (2002), quant-ph/0203003.

    Google Scholar 

  22. Wolf M.M., Eisert J. (2005) New J. Phys. 7: 93

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK

    Motohisa Fukuda

Authors
  1. Motohisa Fukuda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Motohisa Fukuda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fukuda, M. Simplification of Additivity Conjecture in Quantum Information Theory. Quantum Inf Process 6, 179–186 (2007). https://doi.org/10.1007/s11128-007-0051-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-007-0051-8

Keywords

PACS Numbers

Search

Navigation