Quantum resource degradation theory within the framework of observational entropy decomposition

We introduce a theory of quantum resource degradation grounded in a decomposition of observational entropy, which partitions the total resource into inter-block coherence ($\mathcal{C}_{\text{rel}}$) and intra-block noise ($\mathcal{D}_{\text{rel}}$). Under free operations, the total quantum resource is transformed into classical noise while its overall quantity remains conserved. We demonstrate that the metric $\eta$ functions as a diagnostic indicator, providing a new lens on optimization stagnation, particularly the barren plateau phenomenon in variational quantum algorithms. We substantiate this framework through rigorous mathematical analysis and numerical simulations, and we explore how these channels can be physically implemented in real quantum systems. Our approach offers a unified viewpoint on quantum thermalization, measurement-induced disturbance, and the degradation of quantum advantage in practical devices, while also improving optimization strategies for current and near-term noisy quantum hardware.