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

TL;DR

This work addresses the challenge of scaling Quantum Energy Teleportation (QET) in gapped many-body systems by analyzing the 1D anisotropic XY model, where ground-state correlations decay exponentially and standard QET is thermodynamically infeasible at long distances. It introduces a hierarchical quantum repeater architecture that combines heralded entanglement generation, entanglement swapping, and DEJMPS purification to convert exponential resource costs into polynomial overheads, enabling energy activation over arbitrary distances. The key result is that the repeater protocol sustains a non-vanishing average extractable energy $\langle W \rangle = h$ while achieving polylogarithmic time and polynomial energy scaling. This reframes long-range QET as a viable remote quantum-control resource distribution problem and provides a practical blueprint for scalable quantum energy networks.

Abstract

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.

Figures (9)

• Figure 1: Scalability in QET. (a) The physical constraint: Extractable energy is strictly bounded by exponentially decaying correlations $C(r)$. (b) The monolithic limitation: Direct measurement strategies incur exponentially diverging energy costs to combat fidelity loss. (c) The repeater solution: A hierarchical architecture utilizing swapping and purification ensures polynomial resource scaling, making long-range energy extraction thermodynamically viable.
• Figure 2: Excitation spectrum and energy gap of the XY model. The plot shows the Bogoliubov quasiparticle excitation spectrum $\epsilon_k$ as a function of momentum $k/\pi$. In the paramagnetic phase ($h=1.5 > 1$, solid blue line), a finite energy gap $\Delta = 2(h-1)$ opens at $k=0$. This gap suppresses low-energy excitations and is the direct cause of the exponential decay of ground-state correlations. At the critical point ($h=1.0$, dashed orange line), the gap closes, allowing for the emergence of long-range correlations.
• Figure 3: Scaling analysis of the monolithic protocol. (a) The two components of the protocol's cost. The success probability, $P_{\text{succ}}$ (blue circles, log scale), decays exponentially with chain length $N$, while the energy injected per attempt, $\Delta E_{\text{inj}}$ (green squares, linear scale), grows linearly. (b) The resulting total average energy cost, $\langle E_{\text{total}} \rangle$. This cost, which combines the two factors from plot (a), exhibits a prohibitive exponential growth ($\sim N \cdot 2^N$), creating an insurmountable cost wall.
• Figure 4: The Entanglement swapping operation. To connect two adjacent entangled links (e.g., Alice-Charlie and Charlie-Bob), a Bell State Measurement (BSM) is performed on the two qubits held by the intermediate repeater station (Charlie). This projects the system into a new state where Alice and Bob are directly entangled, effectively extending the range of the entanglement.
• Figure 5: The simple iterative protocol (orange circles), governed by the model in Eq. \ref{['eq:fidelity_decay']}, exhibits exponential fidelity decay. The full repeater protocol with purification (green squares, discussed in Sec. \ref{['subsec:purification']}) is required to counteract this decay.