Quantum probability in decision making from quantum information representation of neuronal states
Open accessAbstract
The recent wave of interest to modeling the process of decision making with the aid of the quantum formalism gives rise to the following question: 'How can neurons generate quantum-like statistical data?' (There is a plenty of such data in cognitive psychology and social science). Our model is based on quantum-like representation of uncertainty in generation of action potentials. This uncertainty is a consequence of complexity of electrochemical processes in the brain; in particular, uncertainty of triggering an action potential by the membrane potential. Quantum information state spaces can be considered as extensions of classical information spaces corresponding to neural codes; e.g., 0/1, quiescent/firing neural code. The key point is that processing of information by the brain involves superpositions of such states. Another key point is that a neuronal group performing some psychological function F is an open quantum system. It interacts with the surrounding electrochemical environment. The process of decision making is described as decoherence in the basis of eigenstates of F. A decision state is a steady state. This is a linear representation of complex nonlinear dynamics of electrochemical states. Linearity guarantees exponentially fast convergence to the decision state.
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Neurons exist in a superposition of states until the collapse of the wave function defines a definite state upon interaction with the soul/spirit particle.
“These neurons exist in a superposition of states until the CWF defines a definite state upon interaction with the SSP (Khrennikov et al., 2018).”
From The collapse of the wave function as the mediator of free will in prime neurons (2025) · cites this paper as Khrennikov et al., 2018
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Cites
Tversky, A., & Kahneman, D. (1974) · Science · doi:10.1126/science.185.4157.1124 · Cited by 28,810 · see citing works
Judgment under Uncertainty: Heuristics and Biases
Tversky, A., & Kahneman, D. (1975) · Utility, Probability, and Human Decision Making · doi:10.1007/978-94-010-1834-0_8 · Cited by 22,650 · see citing works
“Risk, Ambiguity, and the Savage Axioms.”
Ellsberg, D. (1961) · The Quarterly Journal of Economics · doi:10.2307/1884324 · Cited by 7,891 · see citing works
Ryle, G. (2006) · Rowman & Littlefield Publishers eBooks · doi:10.5040/9798216413257.ch-2 · Cited by 6,804 · see citing works
Marr, D. (1982) · Cumulative Index of Computer Aided Architectural Design · Cited by 5,733 · see citing works
Mathematical Foundations of Quantum Mechanics
von Neumann, J. (2018) · Princeton University Press eBooks · doi:10.1515/9781400889921 · Cited by 5,043 · see citing works
Decoherence, einselection, and the quantum origins of the classical
Zurek, W. H. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.715 · Cited by 4,295 · see citing works
Allais, M. (1953) · Econometrica · doi:10.2307/1907921 · Cited by 4,054 · see citing works
Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment.
Tversky, A., & Kahneman, D. (1983) · Psychological Review · doi:10.1037/0033-295x.90.4.293 · Cited by 3,991 · see citing works
Speakable and Unspeakable in Quatum Mechanics
Bell, J. S., & Mermin, N. D. (1988) · Physics Today · doi:10.1063/1.2811599 · Cited by 2,985 · see citing works
(1944) · Andalas University Repository (Andalas University) · Cited by 2,118 · see citing works
Quantum Models of Cognition and Decision
Busemeyer, J., & Bruza, P. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9780511997716 · Cited by 1,066 · see citing works
Multiple neural spike train data analysis: state-of-the-art and future challenges
Brown, E. N., Kass, R. E., & Mitra, P. P. (2004) · Nature Neuroscience · doi:10.1038/nn1228 · Cited by 857 · see citing works
Haven, E. E., & Khrennikov, A. Y. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139003261 · Cited by 588 · see citing works
Self-citationProbabilistic models of cognition: exploring representations and inductive biases
Griffiths, T. L., Chater, N., Kemp, C., Perfors, A., & Tenenbaum, J. B. (2010) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2010.05.004 · Cited by 568 · see citing works
Khrennikov, A. Y. (2010) · Springer eBooks · doi:10.1007/978-3-642-05101-2 · Cited by 560 · see citing works
Self-citationQuantum Models of Cognition and Decision
Busemeyer, J. R., Wang, Z., & Pothos, E. (2015) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780199957996.013.17 · Cited by 550 · see citing works
Self-citationA quantum probability explanation for violations of ‘rational’ decision theory
Pothos, E. M., & Busemeyer, J. R. (2009) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2009.0121 · Cited by 485 · see citing works
Self-citationResearch on hidden variable theories: A review of recent progresses
Genovese, M. (2005) · Physics Reports · doi:10.1016/j.physrep.2005.03.003 · Cited by 462 · see citing works
A quantum theoretical explanation for probability judgment errors.
Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. S. (2011) · Psychological Review · doi:10.1037/a0022542 · Cited by 410 · see citing works
Self-citationThe philosophical writings of Niels Bohr
Mermin, N. D. (1990) · Cambridge University Press eBooks · doi:10.1017/cbo9780511608216.015 · Cited by 329 · see citing works
Operationally Invariant Information in Quantum Measurements
Brukner, Č., & Zeilinger, A. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3354 · Cited by 311 · see citing works
Context effects produced by question orders reveal quantum nature of human judgments
Wang, Z., Solloway, T., Shiffrin, R. M., & Busemeyer, J. R. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1407756111 · Cited by 289 · see citing works
(1994) · Journal of Consciousness Studies · Cited by 216 · see citing works
Axonal Propagation of Simple and Complex Spikes in Cerebellar Purkinje Neurons
Khaliq, Z. M., & Raman, I. M. (2005) · Journal of Neuroscience · doi:10.1523/jneurosci.3045-04.2005 · Cited by 167 · see citing works
Information Dynamics and Open Systems
Ingarden, R. S., Kossakowski, A., & Ohya, M. (1997) · Springer eBooks · doi:10.1007/978-94-017-1882-0 · Cited by 144 · see citing works
Quantum Adaptivity in Biology: From Genetics to Cognition
Asano, M., Khrennikov, A. Y., Ohya, M., Tanaka, Y., & Yamato, I. (2015) · Springer eBooks · doi:10.1007/978-94-017-9819-8 · Cited by 141 · see citing works
Self-citationA Quantum-Bayesian Route to Quantum-State Space
Fuchs, C. A., & Schack, R. (2010) · Foundations of Physics · doi:10.1007/s10701-009-9404-8 · Cited by 134 · see citing works
A Quantum-Bayesian Route to Quantum-State Space
Fuchs, C. A., & Schack, R. (2011) · PhilPapers (PhilPapers Foundation) · Cited by 107 · see citing works
A sub-ensemble theory of ideal quantum measurement processes
ALLAHVERDYAN, A. E., Balian, R., & Nieuwenhuizen, T. M. (2016) · Annals of Physics · doi:10.1016/j.aop.2016.11.001 · Cited by 92 · see citing works
Quantum Dynamics for Classical Systems
Bagarello, F. (2012) · Wiley eBooks · doi:10.1002/9781118400586 · Cited by 92 · see citing works
Linear representations of probabilistic transformations induced by context transitionsPreprint
Khrennikov, A. (2001) · Cited by 92 · see citing works
Self-citationCommentary: Extensional Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment
Lewinski, P. (2015) · Frontiers in Psychology · doi:10.3389/fpsyg.2015.01832 · Cited by 91 · see citing works
Quantum Dynamics for Classical Systems: With Applications of the Number Operator
Bagarello, F. (2012) · Cited by 88 · see citing works
The quantum basis of spatiotemporality in perception and consciousness
Igamberdiev, A. U., & Shklovskiy-Kordi, N. E. (2017) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2017.02.008 · Cited by 78 · see citing works
Linear representations of probabilistic transformations induced by context transitions
Khrennikov, A. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/47/304 · Cited by 74 · see citing works
Self-citationComplementarity in Classical Dynamical Systems
Graben, P. B., & Atmanspacher, H. (2006) · Foundations of Physics · doi:10.1007/s10701-005-9013-0 · Cited by 68 · see citing works
On Selective Influences, Marginal Selectivity, and Bell/CHSH Inequalities
Dzhafarov, E. N., & Kujala, J. V. (2013) · Topics in Cognitive Science · doi:10.1111/tops.12060 · Cited by 65 · see citing works
A quantum-like model of selection behavior
Asano, M., Basieva, I., Khrennikov, A. Y., Ohya, M., & Tanaka, Y. (2016) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2016.07.006 · Cited by 53 · see citing works
Self-citationKhrennikov, A. Y. (2011) · Biosystems · doi:10.1016/j.biosystems.2011.05.014 · Cited by 47 · see citing works
Self-citationOzawa, M. (2005) · Annals of Physics · doi:10.1016/j.aop.2005.08.007 · Cited by 47 · see citing works
Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory
Ozawa, M. (2016) · New Generation Computing · doi:10.1007/s00354-016-0205-2 · Cited by 44 · see citing works
Spike propagation and conduction failure in the rat neural lobe.
Dyball, R. E. J., Grossmann, R., Leng, G., & Shibuki, K. (1988) · The Journal of Physiology · doi:10.1113/jphysiol.1988.sp017160 · Cited by 41 · see citing works
Neural implementation of operations used in quantum cognition
Busemeyer, J. R., Fakhari, P., & Kvam, P. (2017) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2017.04.007 · Cited by 41 · see citing works
Operational Axioms for Quantum Mechanics
D’Ariano, G. M. (2007) · AIP conference proceedings · doi:10.1063/1.2713449 · Cited by 40 · see citing works
Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory
Ozawa, M. (2016) · PhilPapers (PhilPapers Foundation) · Cited by 39 · see citing works
Haven, E. E., & Khrennikov, A. Y. (2016) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2016.02.005 · Cited by 38 · see citing works
Self-citationOn creative machines and the physical origins of freedom
Briegel, H. J. (2012) · Scientific Reports · doi:10.1038/srep00522 · Cited by 37 · see citing works
Bagarello, F., Basieva, I., Pothos, E. M., & Khrennikov, A. Y. (2018) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2018.03.004 · Cited by 35 · see citing works
Self-citationQuantum perfect correlationsPreprint
Ozawa, M. (2005) · Cited by 34 · see citing works
Determinism Is Ontic, Determinability is EpistemicPreprint
Harald Atmanspacher, A. (2001) · PhilSci-Archive (University of Pittsburgh) · Cited by 31 · see citing works
A model of differentiation in quantum bioinformatics
Asano, M., Basieva, I., Khrennikov, A. Y., & Yamato, I. (2017) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2017.05.013 · Cited by 24 · see citing works
Self-citationAre quantum-mechanical-like models possible, or necessary, outside quantum physics?
Plotnitsky, A. (2014) · Physica Scripta · doi:10.1088/0031-8949/2014/t163/014011 · Cited by 21 · see citing works
State Entropy and Differentiation Phenomenon
Asano, M., Basieva, I., Pothos, E. M., & Khrennikov, A. Y. (2018) · Entropy · doi:10.3390/e20060394 · Cited by 7 · see citing works
Self-citationFoundational Problems of Quantum Mechanics
Asano, M., Khrennikov, A. Y., Ohya, M., Tanaka, Y., & Yamato, I. (2015) · Springer eBooks · doi:10.1007/978-94-017-9819-8_9 · Cited by 1 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 3
- [2]Plotnitsky, A. Quantum atomicity and quantum information: Bohr, Heisenberg, and quantum mechanics as an information theory. In Quantum theory: reconsideration of foundations, 2002, pp. 309–343.
- [7]Svozil, K. Quantum logic (Discrete Mathematics and Theoretical Computer Science), (Springer, Heidelberg-Berlin, 1998)
- [29]Penrose, R. The Emperor’s new mind. (Oxford Univ. Press, New-York, 1989)
Cited by
Sorted by citations
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-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
“Additionally, in [55], mental information was represented quantum-like through the distribution of action potentials in neuron networks.”
Self-citationQuantum-Inspired and Non-Classical Approaches to Consciousness: Models, Evidence and Constraints
Arias-Carrión, O., Ortega-Robles, E., & Manjarrez, E. (2026) · Brain Sciences · doi:10.3390/brainsci16040386 · Cited by 1 · see citing works
“Models based on a quantum information representation of neuronal states suggest that the intrinsic uncertainty in electrochemical processes—such as stochastic ion-channel dynamics and variability in action potential generation—can be mapped onto superposition-like informational states [47].”
The collapse of the wave function as the mediator of free will in prime neurons
Loboguerrero, D. A. (2025) · Frontiers in Neuroscience · doi:10.3389/fnins.2025.1637217
- Authors
- Khrennikov, A., Basieva, I., Pothos, E. M., & Yamato, I.
- Affiliations
- ITMO University (RU)
- City, University of London (GB)
- Chiba University (JP)
- Corresponding author
- Khrennikov, Andrei
- Venue
- Scientific Reports
- Published
- 2018-11-01
- Volume
- 8
- Issue
- 1
- Pages
- 16225-16225
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC6212453
- OpenAlex
- W2898390164
- Cited by
- 93
- References
- 55
- Citations by year
- 2026: 18 · 2025: 14 · 2024: 14 · 2023: 13 · 2022: 8 · 2021: 8 · 2020: 11 · 2019: 7
- FWCI
- 3.01
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- City Research Online (City University London) (acceptedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Funders
- Leverhulme Trust (RPG-2015, 696331, RPG-2015-311)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
- Physical Sciences › Computer Science › Artificial Intelligence › Cognitive Computing and Networks
- Keywords
- quantum decision making, quantum-like models, action potential generation, neural code, open quantum systems, decoherence
- MeSH terms
- Algorithms, Decision Making, Humans, Models, Psychological, Models, Theoretical, Neurons, Quantum Theory
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