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arXiv:2601.18718 · Physics Letters A

Nontrivial bounds on extractable energy in quantum energy teleportation for gapped manybody systems with a unique ground state

Taisanul Haque

quant-phcond-mat.str-elSubmitted Jan 26, 2026• Announced Jan 27, 2026• 2 citations
v1 · Jan 26, 2026v2 · Mar 24, 2026
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Abstract

We establish a universal, exponentially decaying upper bound on the average energy that can be extracted in quantum energy teleportation (QET) protocols executed on finite-range gapped lattice systems possessing a unique ground state. Under mild regularity assumptions on the Hamiltonian and uniform operator-norm bounds on the local measurement operators, there exist positive constants $C$ and $μ$ (determined by the spectral gap, interaction range and local operator norms) such that for any local measurement performed in a region $A$ and any outcome-dependent local unitaries implemented in a disjoint region $B$ separated by distance $d=\operatorname{dist}(A,B)$ one has $|E_A-E_B|\le C\,e^{-μd}.$ The bound is nonperturbative, explicit up to model-dependent constants, and follows from the variational characterization of the ground state combined with exponential clustering implied by the spectral gap.

Journal reference
Phys. Lett. A 584 (2026) 1316132
DOI
10.1016/j.physleta.2026.131613
Comments
4 pages + Under review in Physics Letters A

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We establish a universal, exponentially decaying upper bound on the average energy that can be extracted in quantum energy teleportation (QET) protocols executed on finite-range gapped lattice systems possessing a unique ground state. Under mild regularity assumptions on the Hamiltonian and uniform operator-norm bounds on the local measurement operators, there exist positive constants CCC and μμμ (determined by the spectral gap, interaction range and local operator norms) such that for any local measurement performed in a region AAA and any outcome-dependent local unitaries implemented in a disjoint region BBB separated by distance d=dist⁡(A,B)d=\operatorname{dist}(A,B)d=dist(A,B) one has ∣EA−EB∣≤C e−μd.|E_A-E_B|\le C\,e^{-μd}.∣EA​−EB​∣≤Ce−μd. The bound is nonperturbative, explicit up to model-dependent constants, and follows from the variational characterization of the ground state combined with exponential clustering implied by the spectral gap.
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.
We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as r−pr^{-p}r−p in ddd dimensions, we prove an error bound O(R−(p−d))O(R^{-(p-d)})O(R−(p−d)) for p>2dp>2dp>2d, where RRR is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.
Many-body quantum systems in the ground states have zero-point energy due to the uncertainty relation. In many cases, the system in the ground state accompanies spatially entangled energy density fluctuation via the noncommutativity of the energy density operators, though the total energy takes a fixed value, i.e., the lowest eigenvalue of the Hamiltonian. Quantum energy teleportation (QET) is a protocol for the extraction of the zero-point energy out of one subsystem using information of a remote measurement of another subsystem. From an operational viewpoint of protocol users, QET can be regarded as an effective rapid energy transportation without breaking all physical laws, including causality and local energy conservation. In the protocol, the ground-state entanglement plays a crucial role. In this paper, we show analytically for a general class of spin-chain systems that the entanglement entropy is lower bounded by a positive quadratic function of the teleported energy between the regions of a QET protocol. This supports a general conjecture that ground-state entanglement is an evident physical resource for energy transportation in the context of QET. The result may also deepen our understanding of the energy density fluctuation in condensed-matter systems from a perspective of quantum information theory.
We consider bulk-gapped fermion systems whose infinite-volume bulk is obtained by adding sufficiently weak even many-body interactions to a free Hamiltonian with spectral gap g>0g>0g>0, allowing polynomial spatial decay of both parts. We prove quantitative local determination of low-energy states: whenever another interaction agrees with the bulk interaction inside a finite or infinite region UUU, with bulk terms crossing its boundary unchanged or removed, all its states with excitation energies in [0,3g/4][0,3g/4][0,3g/4] have local expectations close to those of the bulk ground state deep inside UUU. The error decays with the distance to the complement of UUU, independently of the interaction terms supported outside UUU and of the chosen low-energy state. Quantitative local determination has strong consequences. (i) The bulk interaction has a unique algebraic ground state. (ii) A strong "local perturbations perturb locally" (LPPL) principle holds: arbitrary distant defects change local ground-state expectations only by a spatially decaying error. (iii) Low-energy excitations in finite samples remain localized near the boundary for all times, up to spatially decaying tails, uniformly over arbitrary even boundary terms. (iv) Correlations from deep inside UUU to outside UUU are small, with quantitative bounds in terms of spatial separation and distance to UcU^cUc. To prove local determination of low-energy states, we combine quasi-adiabatic transport of the free ground state to the interacting bulk ground state with a new condition, local excitation detectability (LED). A companion paper establishes gap stability and constructs the transport for weak interactions, while we prove LED at sufficiently weak coupling. The abstract theorem is nonperturbative and applies whenever the transport and LED hypotheses hold.
Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine--Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice U(1)U(1)U(1) selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free (Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs.