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Quantum Model for Psychological Measurements: From the Projection Postulate to Interference of Mental Observables Represented As Positive Operator Valued Measures
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling Phys & Cognit Sci)ORCID iD: 0000-0002-9857-0938
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling Phys & Cognit Sci)
2014 (English)In: NeuroQuantology, ISSN 1303-5150, Vol. 12, no 3, 324-336 p.Article in journal (Refereed) Published
Abstract [en]

Recently foundational issues of applicability of the formalism of quantum mechanics (QM) to cognitive psychology, decision making, and psychophysics attracted a lot of interest. In particular, in (Khrennikov et al., 2014) the possibility to use of the projection postulate and representation of "mental observables" by Hermitian operators was discussed in very detail. The main conclusion of the recent discussions on the foundations of "quantum(-like) cognitive psychology" is that one has to be careful in determination of conditions of applicability of the projection postulate as a mathematical tool for description of measurements of observables represented by Hermitian operators. To represent some statistical experimental data (both physical and mental) in the quantum(-like) way, one has to use generalized quantum observables given by positive operator-valued measures (POVMs). This paper contains a brief review on POVMs which can be useful for newcomers to the field of quantum(-like) studies. Especially interesting for cognitive psychology is a variant of the formula of total probability (FTP) with the interference term derived for incompatible observables given by POVMs. We present an interpretation of the interference term from the psychological viewpoint. As was shown before, the appearance of such a term (perturbing classical FTP) plays the important role in cognitive psychology, e.g., recognition of ambiguous figures and the disjunction effect. The interference term for observables given by POVMs has much more complicated structure than the corresponding term for observables given by Hermitian operators. We elaborate cognitive interpretations of different components of the POVMs-interference term and apply our analysis to a quantum(-like) model of decision making.

Place, publisher, year, edition, pages
2014. Vol. 12, no 3, 324-336 p.
Keyword [en]
quantum model, psychological measurements, projection postulate, decision making
National Category
Neurology Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-38156DOI: 10.14704/nq.2014.12.3.750ISI: 000343114900001Scopus ID: 2-s2.0-84907468518OAI: oai:DiVA.org:lnu-38156DiVA: diva2:763007
Available from: 2014-11-13 Created: 2014-11-13 Last updated: 2016-12-13Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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