quantum-like-mental-markers - SKILL.md Agent Skill

name: quantum-like-mental-markers description: Quantum-informational modeling of mental markers using the I-field (information field) approach. Applies Hilbert space formalism to model contextuality, incompatibility of mental observables, and entanglement-like correlations in cognition and decision-making. Does NOT assume physical quantum processes in the brain. Use when: quantum-like cognition, mental contextuality, decision dynamics, quantum cognition modeling, I-field theory, mental markers.

Quantum-Like Mental Markers: Contextuality and Intra-System Entanglement

Description

A quantum-informational model of mental markers within the I-field (information field) approach. Uses Hilbert space formalism to describe non-classical features of cognition — contextuality, incompatibility of mental observables, and entanglement-like correlations — without assuming physical quantum processes in the brain. This is "quantum-like" modeling (QLM), not quantum physics in the brain.

Source: arXiv:2603.03358 — "Contextuality, Incompatibility, and Intra-System Entanglement of Mental Markers" (Khrennikov, Benninger, Shor, 2026-02-27)

Activation Keywords

quantum-like cognition
mental markers quantum
I-field theory
cognitive contextuality
mental observables incompatibility
quantum cognition decision
Khrennikov quantum-like
intra-system entanglement cognition
Hilbert space cognition
量子类认知
心智标记
认知语境性

Core Concepts

1. Quantum-Like Modeling (QLM) vs Physical Quantum Brain

QLM: Uses mathematical formalism of quantum theory (Hilbert spaces, operators) to model cognitive phenomena
NOT: Claiming the brain is a quantum computer or has quantum coherence
Mental states are represented as vectors in Hilbert space
Mental observables are represented as operators

2. Contextuality in Cognition

Measurement outcomes depend on the context (which other measurements are made)
Violates classical probability axioms (Kolmogorov)
Modeled via non-commuting observables in Hilbert space
Explains order effects, conjunction fallacies, and framing effects

3. Incompatibility of Mental Observables

Certain mental measurements cannot be simultaneously defined
Analogous to Heisenberg uncertainty but for cognition
Non-commuting operators represent incompatible questions/decisions
Order of questions matters (order effects)

4. Intra-System Entanglement

Correlations between different mental processes within one system
Not physical entanglement — mathematical structure of entanglement applied to cognition
Explains holistic, non-separable cognitive states
Mental markers can be "entangled" across different cognitive domains

5. I-Field (Information Field)

Broader theoretical framework encompassing the mental marker model
Information as fundamental construct in cognitive modeling
Connects to quantum information theory concepts

Mathematical Framework

Mental State Representation

|ψ⟩ = Σᵢ cᵢ |mᵢ⟩
where |mᵢ⟩ are mental marker basis states
and cᵢ are complex amplitudes

Observable Operators

Â = Σⱼ aⱼ |φⱼ⟩⟨φⱼ|
where â represents a mental observable (question, decision)
and aⱼ are possible outcomes

Contextuality Condition

P(A then B) ≠ P(B then A)
when [Â, B̂] ≠ 0 (non-commuting observables)

Entanglement-Like Correlation

For composite mental system AB:
|ψ_AB⟩ ≠ |ψ_A⟩ ⊗ |ψ_B⟩
(non-separable mental state across domains)

Workflow for Application

Step 1: Identify Cognitive Phenomenon

Look for:
- Order effects in survey responses
- Violation of classical probability (conjunction fallacy)
- Context-dependent decision outcomes
- Non-separable correlations in mental measurements

Step 2: Construct Hilbert Space Model

1. Define basis states for the cognitive system
2. Represent mental states as state vectors
3. Define observables as operators on the space
4. Identify commuting vs. non-commuting observables

Step 3: Compute Predictions

1. Calculate measurement probabilities using Born rule
2. Check for contextuality (non-Kolmogorovian probabilities)
3. Measure incompatibility via commutator norms
4. Quantify entanglement-like correlations

Step 4: Validate Against Data

Compare model predictions with experimental data:
- Survey response patterns
- Decision-making experiments
- Behavioral economics data
- Cognitive psychology experiments

Tools Used

exec: Run quantum-like simulations, compute commutators
read: Load cognitive experiment data
write: Save model parameters and analysis results

Usage Patterns

Pattern 1: Order Effects Analysis

Model survey question order effects:
1. Represent questions Q₁, Q₂ as non-commuting operators
2. Compute P(Q₁ then Q₂) vs P(Q₂ then Q₁)
3. Compare with empirical data
4. Quantify degree of incompatibility

Pattern 2: Contextuality Detection

Test for cognitive contextuality:
1. Design measurement scenarios with different contexts
2. Compute probabilities under each context
3. Check violation of classical probability bounds
4. Model using quantum-like Hilbert space

Pattern 3: Entanglement-Like Correlation

Analyze cross-domain cognitive correlations:
1. Define composite mental system (e.g., emotion × decision)
2. Test for separability of joint state
3. If non-separable: model as entangled state
4. Quantify entanglement measure (e.g., concurrence analog)

Error Handling

Overfitting Risk

QLM models are mathematically flexible — can fit many patterns
Use cross-validation and information criteria (AIC/BIC)
Compare against classical cognitive models as baseline

Physical vs. Quantum-Like Confusion

Always clarify: this is mathematical formalism, not physical quantum processes
Avoid misinterpretation as "quantum consciousness" claims

Model Complexity

Start with simplest Hilbert space (2D qubit analog)
Increase dimension only if data requires it
Use Occam's razor between quantum-like and classical models

Related Skills

quantum-tug-of-war-decision: Quantum decision making models
gksl-quantum-cognition: GKSL master equations for cognition
quantum-like-cognition-gksl: Open-systems quantum-like cognition
extreme-quantum-cognition: Extreme quantum cognition machines

Limitations

QLM is descriptive, not mechanistic — describes patterns but not underlying biology
Model selection challenge: when to use quantum-like vs classical models
Parameter estimation can be non-trivial
Requires careful experimental design to detect contextuality
Not a claim about physical quantum processes in the brain

References

arXiv:2603.03358 — Mental Markers paper (https://arxiv.org/abs/2603.03358)
https://arxiv.org/pdf/2603.03358 — PDF download