Quantum density-matrix framework for opinion dynamics reduces to Friedkin-Johnsen model while capturing ambivalence and order effects

The model treats each agent's state as a density operator whose diagonal encodes expressed opinions and off-diagonal terms quantify ambivalence. Survey items are represented as non-commuting observables, so sequential measurements naturally produce order effects absent from classical scalar or vector formulations. Under a product-state approximation the dynamics collapse exactly to the Friedkin-Johnsen update rule, recovering the classical limit while retaining additional observables such as pairwise opinion covariances.

Synthetic and real-world network simulations reveal that pairwise correlations exhibit topology-dependent transients yet converge to identical steady states; quantum coherence, by contrast, decays exponentially at a rate fixed by the Hamiltonian and independent of network structure. This separation supplies a measurable signature that classical models cannot generate.

The work bridges quantum cognition research with network science by importing tools previously applied to decision-making paradoxes into multi-agent settings. Earlier quantum-social papers remained largely individual-level; here the network supplies the interaction graph, enabling direct comparison against empirical opinion time series once coherence or covariance measurements become feasible.

Next steps require laboratory or panel surveys that interleave question order and track response consistency at the individual level to test whether observed order-effect magnitudes match the predicted non-commutativity scale.