quantum-tug-of-war-decision

name

quantum-tug-of-war-decision

description

Quantum Tug-of-War (QTOW) decision making model — contextuality arises generatively from physically grounded constraints on decision dynamics. Conservation-based internal state updates and measurement-induced disturbance produce KCBS-type contextuality witnesses. Proves quantum probability is structurally necessary for adaptive decision dynamics, not merely descriptive. Use when: quantum decision making, contextuality in choices, TOW model, non-Kolmogorovian probability, adaptive learning dynamics, measurement-induced disturbance, arXiv:2601.10034.

Quantum Tug-of-War Decision Making

Theoretical framework where contextuality in decision making arises generatively from physically grounded constraints, not from assumed quantum probability.

Core Insight

Contextuality is a structural consequence of adaptive learning dynamics:

• Conservation-based internal state updates
• Measurement-induced disturbance
• Together preclude any non-contextual classical description

The TOW Model

Classical Tug-of-War (TOW)

Decision as resource allocation between competing options:

• Each option has an associated value/reward
• Agent allocates internal resources (attention, effort)
• Conservation law: total resource is fixed

Quantum Extension

Internal state → quantum density matrix ρ Choice → projective measurement on ρ Update → post-measurement state transformation

Key: measurement changes the state, creating path dependence that no single classical hidden variable can explain.

KCBS Contextuality Witness

The model admits Klyachko-Can-Binicioglu-Shumovsky (KCBS) type contextuality witnesses in a minimal single-system setting:

⟨A₁A₂⟩ + ⟨A₂A₃⟩ + ⟨A₃A₄⟩ + ⟨A₄A₅⟩ + ⟨A₅A₁⟩ ≥ -3 (classical bound)

Quantum systems can violate this bound, demonstrating contextuality.