Nontrivial bounds on extractable energy in quantum energy teleportation for gapped manybody systems with a unique ground state
Taisanul Haque
TL;DR
This work proves a universal, nonperturbative upper bound on the net energy extractable via Quantum Energy Teleportation (QET) in finite-range gapped lattice systems with a unique ground state: the energy difference between sender and receiver obeys $|E_A-E_B|\le C e^{-\mu d}$, where $d$ is the separation and $C,\mu$ are set by the spectral gap, interaction range, and local operator norms. The authors combine a variational reduction with exponential clustering (via Lieb-Robinson bounds and the gap) and a careful local-decomposition analysis to bound cross-region correlations, showing that local measurements perturb the ground state only in a finite neighbourhood and that classical communication cannot overcome this to achieve substantial energy transfer at large $d$. A refinement using commutator structure of decoding unitaries yields potentially tighter prefactors when $U_a$ has a local generator. The results provide rigorous justification for the locality of QET effects and offer a route to compute explicit constants for specific models, with potential extensions to thermal states and more general quantum operations.
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.