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

This paper addresses a central conceptual challenge in Quantum-like Cognition and Decision-Making (QCDM) and the broader research program of Quantum-like Modeling (QLM): the interpretation of phases in quantum-like state superpositions. In QLM, system states are represented by normalized vectors in a complex Hilbert space, $|\psi ⟩={\sum }_k{X}_k|k⟩$, where the squared amplitudes $P_k={\left|X_k\right|}^2$ are outcome probabilities. However, the meaning of the phase factors $e^{i{\varphi }_k}$ in the coefficients $X_k=P_k{e}^{i{\varphi }_k}$ 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.