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

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

URL: http://arxiv.org/abs/2503.05859v1
Date: Fri, 07 Mar 2025 18:30:44 GMT
Title: Quantum-like cognition and decision making in the light of quantum measurement theory
Authors: Miho Fuyama, Andrei Khrennikov, Masanao Ozawa,
Abstract summary: We characterize the class of quantum measurements that matches the applications of quantum theory to cognition.<n>We highlight the role of it noncommutativity of the state update maps generated by measurement back action''<n>We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 SR\bar{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 ${\cal SR\bar{P}}$ 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.

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