Quantum-like Cognition and Decision Making: Interpretation of Phases in Quantum-like Superposition

Emmanuel E. Haven, Andrei Yu. Khrennikov

Mehrdad Ashtiani, Mohammad Abdollahi Azgomi

Andrei Yu. Khrennikov

Andrei Yu. Khrennikov

: the interpretation of phases in quantum-like state superpositions. In QLM, system states are represented by normalized vectors in a complex Hilbert space, |ψ⟩=∑kXk|k⟩, where the squared amplitudes Pk=|Xk|2 are outcome probabilities. However, the meaning of the phase factors eiϕk in the coefficients Xk=Pkeiϕk has remained elusive, often treating them as purely phenomenological parameters. This practice, while successful in describing cognitive interference effects (the "interference of the mind"), has drawn criticism for expanding the model's parameter space without a clear physical or cognitive underpinning. Building on a recent framework that connects QCDM to neuronal network activity, we propose a concrete interpretation. We argue that the phases in quantum-like superpositions correspond directly to the phases of random oscillations generated by neuronal circuits in the brain. This interpretation not only provides a natural, non-phenomenological basis for phase parameters within QCDM but also helps to bridge the gap between quantum-like models and classical neurocognitive frameworks, offering a consistent physical analogy for the descriptive power of QLM.

Ada Öztürkmen

Classical models of decision-making under uncertainty, grounded in expected utility theory and Bayesian probability, often fail to account for systematic cognitive anomalies such as preference reversals, order effects, ambiguity aversion, and context-dependent choices. Quantum cognition models offer a novel theoretical framework that applies the mathematical principles of quantum probability—such as superposition, interference, and non-commutativity—to cognitive processes without assuming physical quantum mechanisms in the brain. By representing cognitive states as probabilistic superpositions that collapse through decision “measurements,” these models provide parsimonious explanations for violations of classical rationality. This paper examines how quantum cognition frameworks capture contextual influence, belief updating, and interference effects in uncertain decision environments. Drawing on findings from cognitive psychology and behavioral economics, the study highlights the relevance of quantum cognition for applications in economic choice modeling, legal decision analysis, and artificial intelligence. The analysis suggests that quantum probability offers a robust alternative to classical approaches when modeling human decision-making in complex, ambiguous, and context-sensitive situations.

Andrei Yu. Khrennikov