  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 protocols for 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 protocols, 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 new perspective of quantum information theory.
