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On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements
Prokhorov Gen Phys Inst, Russia.ORCID iD: 0000-0003-2396-6193
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, p. 1379-1393Article in journal (Refereed) Published
Abstract [en]

In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility () (the standard perfect repeatability) and separated reproducibility(). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, , is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

Place, publisher, year, edition, pages
2015. Vol. 45, no 10, p. 1379-1393
Keywords [en]
Order effect, Repeatability, Quantum-like models, POVMs in cognitive science
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-46896DOI: 10.1007/s10701-015-9932-3ISI: 000361898600015Scopus ID: 2-s2.0-84942503859OAI: oai:DiVA.org:lnu-46896DiVA, id: diva2:865068
Available from: 2015-10-26 Created: 2015-10-26 Last updated: 2018-05-16Bibliographically approved

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Basieva, IrinaKhrennikov, Andrei

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