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On the equivalence of the Clauser-Horne and Eberhard inequality based tests
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
Univ Vienna, Vienna, Austria ; Cornell Univ, Ithaca, USA .ORCID iD: 0000-0002-7801-4440
Austrian Acad Sci, Vienna, Austria.
Austrian Acad Sci, Vienna, Austria ; Univ Vienna, Vienna, Austria .
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2014 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, 014019Article in journal (Refereed) Published
Abstract [en]

Recently, the results of the first experimental test for entangled photons closing the detection loophole (also referred to as the fair sampling loophole) were published (Vienna, 2013). From the theoretical viewpoint the main distinguishing feature of this long-aspired to experiment was that the Eberhard inequality was used. Almost simultaneously another experiment closing this loophole was performed (Urbana-Champaign, 2013) and it was based on the Clauser-Horne inequality (for probabilities). The aim of this note is to analyze the mathematical and experimental equivalence of tests based on the Eberhard inequality and various forms of the Clauser-Horne inequality. The structure of the mathematical equivalence is nontrivial. In particular, it is necessary to distinguish between algebraic and statistical equivalence. Although the tests based on these inequalities are algebraically equivalent, they need not be equivalent statistically, i.e., theoretically the level of statistical significance can drop under transition from one test to another (at least for finite samples). Nevertheless, the data collected in the Vienna test implies not only a statistically significant violation of the Eberhard inequality, but also of the Clauser-Horne inequality (in the ratio-rate form): for both a violation > 60 sigma.

Place, publisher, year, edition, pages
2014. Vol. T163, 014019
Keyword [en]
loophole free test, Bell inequality, Eberhard inequality, Clauser-Horne inequality, confidence interval, Chebyshev inequality, non-Gaussian distributions
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-41401DOI: 10.1088/0031-8949/2014/T163/014019ISI: 000349832400020OAI: oai:DiVA.org:lnu-41401DiVA: diva2:798335
Available from: 2015-03-26 Created: 2015-03-26 Last updated: 2016-05-03Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
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