Exploring quantum Heider balance theory

This work generalizes Heider's classical balance theory into a quantum mechanical framework. The core idea is that, just as quantum reality exists in a superposition of possibilities until observed, our real-life social relationships often exist in a subjective superposition of balanced and imbalanced triads, experiencing both stress and relief simultaneously. As classical physics limits our ability to observe these 'entangled' states, we introduced a quantum generalization involving creation and annihilation operators, as well as a new Hamiltonian. This approach reveals inherent, lifelike states within the balance theory that are simply unobservable under classical limitations. Examining the ground and stable states in quantum evolution under disorder (temperature) reveals a transition point from balanced states to a random phase. Our results reveal new dynamic behaviors that are unique to quantum social systems and offer new insights into collective decision-making, conflict resolution and the emergence of order in complex networks.