Statistical Analysis of QKD Networks in Real-Life Environment

  • K. LessiakEmail author
  • J. PilzEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 797)


As discussed before, Quantum Key Distribution (QKD) has already been realized in various experiments. Due to this there is an interest to prove whether or not external influences like temperature, humidity, sunshine duration, and global radiation have an effect on the quality of QKD systems. In consequence there is also an interest to predict the qubit error rate (QBER) and the key rate (KR).


Generalize Linear Model Generalize Linear Mixed Model Exponential Family Global Radiation Sunshine Duration 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson, T.W.: On the distribution of the two-sample Cramer-von mises criterion. Ann. Math. Stat. 33(3), 1148–1159 (1962)zbMATHCrossRefGoogle Scholar
  2. 2.
    Demidenko, E.: Mixed Models. WILEY, Hoboken, NJ (2004)CrossRefGoogle Scholar
  3. 3.
    Fahrmeir, L., Kneip, T., Lang, S.: Regression. Springer Verlag, Berlin (2007)Google Scholar
  4. 4.
    Faraway, J.J.: Extending the Linear Model with R. Chapman & Hall/CRC, Boca Raton, FL (2006)Google Scholar
  5. 5.
    Lessiak, K., Kollmitzer, C., Schauer, S., Pilz, J., Rass, S.: Statistical Analysis of QKD Networks in Real-life Environments. Third International Conference on Quantum, Nano and Micro Technologies (2009)Google Scholar
  6. 6.
    McCullagh, P., Nelder, J.: Generalized Linear Models, 2nd ed. Monographs on Statistics and Applied Probability 37. Chapman & Hall, London (1989)zbMATHGoogle Scholar
  7. 7.
    Nelder, J.A., Wedderburn, R.: Generalized linear models. J. R. Stat. Soc. A 135(3), 370–384 (1972)CrossRefGoogle Scholar
  8. 8.
    Pinheiro, J.C., Bates, D.M.: Approximations to the log-likelihood function in the nonlinear mixed-efffects model. J. Comput. Graph. Stat. 4(1), 12–35 (1995)CrossRefGoogle Scholar
  9. 9.
    Pinheiro, J.C., Bates, D.M.: Mixed Effects Models in s and s-plus. Springer Verlag, New York (2000)Google Scholar
  10. 10.
    Poppe, A., Peev, M., Maurhart, O.: Outline of the SECOQC Quantum-Key-Distribution Network in Vienna. Int. J. of Quant. Inf. 6(2), 209–218 (2008)CrossRefGoogle Scholar
  11. 11.
    Sinha, S.K.: Robust analysis of generalized linear mixed models. J. Am. Stat. Assoc. 99, 451–460 (2004)zbMATHCrossRefGoogle Scholar
  12. 12.
    Tierney, L., Kadane, J.B.: Accurate approximations for posterior moments and marginal densities. J. Am. Stat. Assoc. 81, 82–86 (1986)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Verbeke, G., Molenberghs, G.: Linear Mixed Models for Longitudinal Data. Springer Verlag, New York (2000)Google Scholar
  14. 14.
    Verbeke, G., Molenberghs, G.: Models for Discrete Longitudinal Data. Springer Verlag, New York (2005)Google Scholar
  15. 15.
    Wolfinger, R., O’Connell, M.: Generalized linear mixed models: A pseudo-likelihood approach. J. Stat. Comput. Simul. 48, 233–243 (1993)zbMATHCrossRefGoogle Scholar
  16. 16.
    Wood, S.N.: Generalized Additive Models. Chapman & Hall/CRC, Boca Ration, FL (2006)Google Scholar
  17. 17.
    Zeger, S.L., Liang, K.Y., Albert, P.S.: Models for longitudinal data: A generalized estimating equation approach. Biometrics 44(4), 1049–1060 (1988)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Safety & Security Department, Quantum TechnologiesAIT Austrian Institute of Technology GmbHKlagenfurtAustria
  2. 2.Institute of StatisticsKlagenfurt UniversityKlagenfurtAustria

Personalised recommendations