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Unconditional Quantum Correlations do not Violate Bell's Inequality
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling Phys Engn Econ & Cognit Sci)ORCID iD: 0000-0002-9857-0938
2015 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 10, 1179-1189 p.Article in journal (Refereed) Published
Abstract [en]

In this paper I demonstrate that the quantum correlations of polarization (or spin) observables used in Bell's argument against local realism have to be interpreted as conditional quantum correlations. By taking into account additional sources of randomness in Bell's type experiments, i.e., supplementary to source randomness, I calculate (in the standard quantum formalism) the complete quantum correlations. The main message of the quantum theory of measurement (due to von Neumann) is that complete correlations can be essentially smaller than the conditional ones. Additional sources of randomness diminish correlations. One can say another way around: transition from unconditional correlations to conditional can increase them essentially. This is true for both classical and quantum probability. The final remark is that classical conditional correlations do not satisfy Bell's inequality. Thus we met the following conditional probability dilemma: either to use the conditional quantum probabilities, as was done by Bell and others, or complete quantum correlations. However, in the first case the corresponding classical conditional correlations need not satisfy Bell's inequality and in the second case the complete quantum correlations satisfy Bell's inequality. Thus in neither case we have a problem of mismatching of classical and quantum correlations. The whole structure of Bell's argument was based on identification of conditional quantum correlations with unconditional classical correlations.

Place, publisher, year, edition, pages
2015. Vol. 45, no 10, 1179-1189 p.
Keyword [en]
Conditional and unconditional correlations, Quantum and classical correlations, Bell's inequality, Quantum measurement theory, Random generators
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-46893DOI: 10.1007/s10701-015-9930-5ISI: 000361898600004OAI: oai:DiVA.org:lnu-46893DiVA: diva2:865050
Available from: 2015-10-26 Created: 2015-10-26 Last updated: 2016-05-03Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • text
  • asciidoc
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