Quantum Models for Psychological Measurements: An Unsolved Problem
Open accessAbstract
There has been a strong recent interest in applying quantum theory (QT) outside physics, including in cognitive science. We analyze the applicability of QT to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a given question is expected to be repeated if the question is posed again, irrespective of whether another question is asked and answered in between. The second property (question order effect) is that the response probabilities frequently depend on the order in which the questions are asked. Whenever these two properties occur together, it poses a problem for QT. The conventional QT with Hermitian operators can handle response replicability, but only in the way incompatible with the question order effect. In the generalization of QT known as theory of positive-operator-valued measures (POVMs), in order to account for response replicability, the POVMs involved must be conventional operators. Although these problems are not unique to QT and also challenge conventional cognitive theories, they stand out as important unresolved problems for the application of QT to cognition. Either some new principles are needed to determine the bounds of applicability of QT to cognition, or quantum formalisms more general than POVMs are needed.
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In QPT, sequential joint probability exhibits QOE if and only if it does not exhibit RRE.
“Conversely, in QPT, sequential joint probability exhibits QOE if and only if it does not exhibit RRE (Khrennikov et al., 2014; Ozawa & Khrennikov, 2023).”
From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Khrennikov et al., 2014
In Theory §4 (page unavailable), Propositions 2–3 say that, under their stated conditions, repeat-response stability requires commuting observables, and commuting observables produce no question-order effect. This supports the direction that a question-order effect rules out repeat-response stability. The paper does not establish the converse: absence of repeat-response stability does not, by itself, imply a question-order effect. (LLM, conf=0.86)
Experimental — accuracy not yet measuredSequential joint probability in CPT exhibits the response replicability effect but not the question order effect.
“Regarding the question order effect (QOE) and the response replicability effect (RRE), sequential joint probability in CPT exhibits RRE but not QOE.”
From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Khrennikov et al., 2014
The Conclusions state that, in conventional quantum theory, accounting for response replicability requires commuting observables, which predict no question-order effect in sequential joint probabilities. The paper does not establish this claim for CPT (classical probability theory); its stated result concerns QT. (LLM, conf=0.83)
Experimental — accuracy not yet measuredIn Khrennikov et al. (2014), it was demonstrated that a projection-based description cannot be combined with the response replicability effect.
“However, in Khrennikov et al. (2014), it was demonstrated that such a projection-based description cannot be combined with another psychological effect, the response replicability effect.”
From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Khrennikov et al. (2014)
The Conclusions (page unavailable) say that a projection-based explanation of the question-order effect requires noncommuting observables, which cannot also account for repeated answers to repeated questions. But the paper also says that conventional quantum theory can handle response replicability on its own. The incompatibility applies to a projection-based account of both effects, not to every projection-based description. (LLM, conf=0.86)
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Cites
Quantum-like brain: Interference of minds
Khrennikov, A. (2006) · Biosystems · doi:10.1016/j.biosystems.2005.11.005 · Cited by 155 · see citing works
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Pothos, E. M., & Busemeyer, J. R. (2022) · Annual Review of Psychology · doi:10.1146/annurev-psych-033020-123501 · Cited by 184 · see citing works
Self-citationQuantum-like modeling of cognition
Khrennikov, A. (2015) · Frontiers in Physics · doi:10.3389/fphy.2015.00077 · Cited by 91 · see citing works
Self-citationOzawa, M., & Khrennikov, A. (2021) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2020.102491 · Cited by 55 · see citing works
Self-citationCoupling quantum-like cognition with the neuronal networks within generalized probability theory
Khrennikov, A., Ozawa, M., Benninger, F., & Shor, O. (2025) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2025.102923 · Cited by 17 · see citing works
“However, in [53], it was demonstrated that such a projection-based description cannot be combined with another psychological effect, the response replicability effect.”
Self-citationSwan, M., dos Santos, R. P., & Witte, F. (2022) · Quantum Reports · doi:10.3390/quantum4010008 · Cited by 16 · see citing works
Quantum formalism for the dynamics of cognitive psychology
Brody, D. C. (2023) · Scientific Reports · doi:10.1038/s41598-023-43403-4 · Cited by 13 · see citing works
- Authors
- Khrennikov, A., Basieva, I., Dzhafarov, E. N., & Busemeyer, J. R.
- Affiliations
- Linnaeus University (SE)
- Purdue University West Lafayette (US)
- Indiana University Bloomington (US)
- Corresponding author
- Dzhafarov, Ehtibar N.
- Venue
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2014-10-24
- Volume
- 9
- Issue
- 10
- Pages
- e110909
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC4208824
- OpenAlex
- W2060765444
- Cited by
- 123
- References
- 1
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 3 · 2023: 12 · 2022: 16 · 2021: 7 · 2020: 5 · 2019: 4 · 2018: 4 · 2017: 15 · 2016: 21 · 2015: 16 · 2014: 6
- FWCI
- 9.62
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS ONE (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- City Research Online (City University London) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1155956, FA9550-12-1-0397)
- Linnéuniversitetet
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Keywords
- quantum cognition, quantum measurement, question order effects, public opinion survey, POVM, Hermitian operators, psychological measurement
- MeSH terms
- Humans, Models, Psychological, Quantum Theory
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