Journal of Russian Laser Research

, Volume 36, Issue 1, pp 2–16 | Cite as

Modeling Tests Based on the Eberhard Inequality

  • Polina Titova
  • Andrei Khrennikov


Last year, the first experimental tests closing the detection loophole (also referred to as the fair sampling loophole) were performed by two experimental groups, one in Vienna and the other one in Urbana-Champaign. To violate the Bell-type inequalities (the Eberhard inequality in the first test and the Clauser–Horne inequality in the second test), one has to optimize a number of parameters involved in the experiment (angles of polarization beam splitters and quantum state parameters). We study this problem for the Eberhard inequality in detail, using the advanced method of numerical optimization, namely, the Nelder–Mead method.


Bell’s test fair sampling loophole Eberhard inequality Clauser–Horne inequality optimization of parameters fluctuations of angles coefficient of variation 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Moscow Institute of Electronic Technology ZelenogradMoscowRussia
  2. 2.International Center for Mathematical Modeling in Physics Engineering, Economics, and Cognitive Science Linnaeus UniversityVäxjöSweden

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