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Analog of Formula of Total Probability for Quantum Observables Represented by Positive Operator Valued Measures
Linnaeus University, Faculty of Technology, Department of Mathematics.
2016 (English)In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 55, no 9, 3859-3874 p.Article in journal (Refereed) Published
Abstract [en]

We represent Born’s rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born’s rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.

Place, publisher, year, edition, pages
2016. Vol. 55, no 9, 3859-3874 p.
Keyword [en]
Atomic instruments, Born rule, Formula of total probability, Interference, Interpretations of quantum mechanics, Positive operator valued measures, Quantum operations
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-56068DOI: 10.1007/s10773-016-3015-xISI: 000380724500007Scopus ID: 2-s2.0-84964270215OAI: oai:DiVA.org:lnu-56068DiVA: diva2:971473
Available from: 2016-09-16 Created: 2016-08-31 Last updated: 2016-09-20Bibliographically approved

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Khrennikov, Andrei
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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
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  • 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
  • rtf