Ground-State Entanglement Bound for Quantum Energy Teleportation of General Spin-Chain Models

TL;DR

This paper proves that in general spin-chain models, the amount of ground-state entanglement sets a lower limit on the energy that can be teleported, highlighting entanglement as a key resource for quantum energy transfer.

Contribution

It analytically establishes a lower bound on entanglement entropy based on the teleported energy in spin-chain systems, supporting the role of entanglement in quantum energy teleportation.

Findings

Entanglement entropy is bounded below by a quadratic function of teleported energy.

Supports the conjecture that ground-state entanglement is essential for energy transport in QET.

Provides insights into energy density fluctuations in condensed matter from a quantum information perspective.

Abstract

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.