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

TL;DR

This paper derives an exponential upper bound on the energy that can be extracted via quantum energy teleportation in gapped many-body systems with a unique ground state, highlighting limitations in energy transfer over distance.

Contribution

It provides a nonperturbative, explicit bound on extractable energy in QET protocols for gapped lattice systems, depending on spectral gap and interaction parameters.

Findings

Energy extraction decays exponentially with distance in gapped systems.

Constants depend on spectral gap, interaction range, and local operator norms.

Bound deteriorates as the spectral gap closes, indicating limitations in gapless regimes.

Abstract

We establish an 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 $\mu$ (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 $|E_A-E_B|\le C\,e^{-\mu d}$. 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. We emphasize that the constants deteriorate as the gap closes (equivalently, as the correlation length diverges), so the estimate is intended for the gapped regime.