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

Miho Fuyama, Andrei Khrennikov, Masanao Ozawa

TL;DR

This paper argues that cognition and decision making cannot be fully captured by projective quantum measurements alone. It introduces sharp repeatable non-projective measurements (SRbar-P) as a suitable framework for modeling advanced cognitive tasks that involve memory, highlighting two distinct forms of noncommutativity: observable-noncommutativity and state-update-noncommutativity. By analyzing QOE, RRE, and QQ-equality, it shows that SRbar-P can reproduce complex cognitive effects even when observables commute, challenging the direct transfer of physical quantum notions to cognition. The work provides a foundation for distinguishing quantum-like cognitive phenomena from physical quantum effects and suggests diagnostic tools for future research.

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.

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

TL;DR

This paper argues that cognition and decision making cannot be fully captured by projective quantum measurements alone. It introduces sharp repeatable non-projective measurements (SRbar-P) as a suitable framework for modeling advanced cognitive tasks that involve memory, highlighting two distinct forms of noncommutativity: observable-noncommutativity and state-update-noncommutativity. By analyzing QOE, RRE, and QQ-equality, it shows that SRbar-P can reproduce complex cognitive effects even when observables commute, challenging the direct transfer of physical quantum notions to cognition. The work provides a foundation for distinguishing quantum-like cognitive phenomena from physical quantum effects and suggests diagnostic tools for future research.

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} - 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 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.

Paper Structure

This paper contains 11 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Detailed explanations and decoding of the blocks of the schematic representation
  3. Mathematical formalism of quantum measurement theory
  4. Non-invasivenss vs. invasiveness
  5. Disjunction, question order and response replicability effects, and QQ-equality
  6. Sharp repeatable non-projective invasive measurements
  7. Quantumness: noncommutativity of observables versus state update maps
  8. ${\cal P}$-class: noncommutativity $\sim$ noncommutativity of observables
  9. ${\cal SR\bar{P}}$-class: nonclassicality $\sim$ noncommutativity of state update maps
  10. State dependence of noncommutativity and classicality
  11. Concluding remarks

Figures (1)

  • Figure 1: Schematic presentation of the structure of measurement theory, classical vs. quantum: (see subsection \ref{['se:caption']} for detailed explanations and decoding of its blocks).