Skip to main content
Log in

Symplectic approach to construction of cyclic and non-cyclic sets of mutually unbiased bases

  • Elementary Particles and Fields Theory
  • Published:
Physics of Atomic Nuclei Aims and scope Submit manuscript

Abstract

We formulate the construction of cyclic and non-cyclic complete sets of mutually unbiased bases, corresponding to the underlyining field and semifield structures, in the framework of the symplectic approach.

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

Access this article

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. J. Schwinger, Proc. Natl. Acad. Sci. USA 46, 570 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  2. I. D. Ivonovic, J. Phys. A 14, 3241 (1981).

  3. T. Durt, B.-G. Englert, I. Bengtsson, and K. Zyczkowski, Int. J. Quantum. Inform. 8, 535 (2010).

    Article  Google Scholar 

  4. W. K. Wootters and B. D. Fields, Ann. Phys. N. Y. 191, 363 (1989)

    Article  ADS  Google Scholar 

  5. W. K. Wootters, Found. Phys. 36, 112 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  6. S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, and V. Vatan, Algorithmica 34, 512 (2002).

    Article  MathSciNet  Google Scholar 

  7. J. Lawrence, C Brukner, and A. Zeilinger, Phys. Rev. A 65, 032320 (2002).

    Article  ADS  Google Scholar 

  8. J. L. Romero, G. Björk, A. B. Klimov, and L. L. Sánchez-Soto, Phys. Rev. A 72, 062310 (2005).

    Article  ADS  Google Scholar 

  9. M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A 69, 062311 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. B. Klimov, C. Munoz, and L. L. Sánchez-Soto, J. Phys. A 45, 215303 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  11. C. Spengler and B. Kraus, Phys. Rev. A 88, 052323 (2013).

    Article  ADS  Google Scholar 

  12. W. M. Kantor, J. Algebra 270, 96 (2003)

  13. J. Math. Phys. 53, 032204 (2012).

  14. A. Garcia, J. L. Romero, and A. B. Klimov, J. Phys. A 43, 385301 (2010).

    Article  MathSciNet  Google Scholar 

  15. A. B. Klimov, J. L. Romero, G. Björk, and L. L. Sánchez-Soto, Ann. Phys. (N. Y.) 324, 53 (2009).

    Article  ADS  Google Scholar 

  16. D. E. Knuth, J. Algebra 2, 182 (1965).

    Article  MathSciNet  Google Scholar 

  17. R. Gow and J. Sheekey, Finite Fields Apps. 17, 194 (2011).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Garcia.

Additional information

The text was submitted by the authors in English.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garcia, A., Klimov, A.B. Symplectic approach to construction of cyclic and non-cyclic sets of mutually unbiased bases. Phys. Atom. Nuclei 80, 549–552 (2017). https://doi.org/10.1134/S1063778817030073

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063778817030073

Navigation