Quantum-like cognition and decision making in the light of quantum measurement theory

2025-03-07

AI Summary

Classical probabilistic models fail to explain cognitive phenomena such as question-order effects and response replicability; it remains unclear which quantum measurement formalism adequately captures these effects. Method: Moving beyond conventional projective measurements, the paper introduces “sharp repeatable non-projective” (SRP̄) measurements—a novel subclass of quantum measurements tailored for cognitive modeling. It integrates positive operator-valued measures (POVMs), instrument formalism, and state-update mappings to rigorously analyze post-measurement dynamics. Contribution/Results: The work demonstrates that cognitive non-classicality arises from non-commutativity in state-updating operations—not from non-commutativity of observables themselves. This clarifies a fundamental distinction between physical quantum measurements and their cognitive analogues, resolving long-standing conceptual ambiguities. Moreover, it establishes a principled interdisciplinary framework bridging foundational quantum theory and cognitive science, enabling theoretically grounded, empirically testable quantum cognitive models.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects, cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely {it sharp repeatable non-projective measurements} - ${cal SRar{P}}. $ This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modeling isn't automatic borrowing of the quantum formalism. Exploring the class ${cal SRar{P}}$ highlights the role of {it noncommutativity of the state update maps generated by measurement back action.} Thus, ``non-classicality'' in quantum physics as well as quantum-like modeling for cognition is based on two different types of noncommutativity, of operators (observables) and instruments (state update maps): {it observable-noncommutativity} vs. {it state update-noncommutativity}. We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.

Problem

• Explores quantum measurements for cognition and decision making.
• Identifies limitations of projective measurements in cognitive effects.
• Introduces sharp repeatable non-projective measurements for quantum-like modeling.

Innovation

• Uses sharp repeatable non-projective measurements
• Explores noncommutativity in state update maps
• Distinguishes quantum-like cognitive effects uniquely