Quantum resource degradation theory within the framework of observational entropy decomposition

TL;DR

This paper develops a quantum resource degradation theory based on observational entropy decomposition, linking resource loss to classical noise and providing insights into optimization challenges in quantum algorithms.

Contribution

It introduces a novel framework decomposing quantum resources into coherence and noise, with implications for understanding quantum thermalization and improving variational quantum algorithm optimization.

Findings

The metric η indicates optimization stagnation and barren plateaus.

The framework unifies concepts of thermalization, measurement disturbance, and resource degradation.

Numerical simulations support the theoretical analysis.

Abstract

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.