Scalable Repeater Architecture for Long-Range Quantum Energy Teleportation in Gapped Systems

Quantum Energy Teleportation (QET) constitutes a paradigm-shifting protocol that permits the activation of local vacuum energy through the consumption of pre-existing entanglement and classical communication. Nevertheless, the implementation of QET is severely impeded by the fundamental locality of gapped many-body systems, where the exponential clustering of ground-state correlations restricts energy extraction to microscopic scales. In this work, we address this scalability crisis within the framework of the one-dimensional anisotropic XY model. We initially provide a rigorous characterization of a monolithic measurement-induced strategy, demonstrating that while bulk projective measurements can theoretically induce long-range couplings, the approach is rendered physically untenable by exponentially diverging thermodynamic costs and vanishing success probabilities. To circumvent this impasse, we propose and analyze a hierarchical quantum repeater architecture adapted for energy teleportation. By orchestrating heralded entanglement generation, iterative entanglement purification, and nested entanglement swapping, our protocol effectively counteracts the fidelity degradation inherent in noisy quantum channels. We establish that this architecture fundamentally alters the operational resource scaling from exponential to polynomial. This proves, for the first time, the physical permissibility and computational tractability of activating vacuum energy at arbitrary distances. The significance lies not in net energy gain, but in establishing long-range QET as a viable protocol for remote quantum control and resource distribution.