Quantum Energy Teleportation and Entropy Change due to Feedback Control in One-Dimensional Heisenberg Model

We study the quantum energy teleportation in a four-spin one-dimensional Heisenberg model. A local magnetic field is applied at the edge sites to control the degree of the ground-state entanglement. In the teleportation protocol, an energy sender performs a projective measurement at one edge site, while an energy receiver performs a feedback control at the other edge site dependent on the measurement result to extract energy. We find that the energy extracted by the receiver takes a maximum at intermediate value of the local magnetic field. We also find that this magnetic-field behavior is almost proportional to entropy changes due to the feedback control. The role of a feedback control in an entropy change is discussed in terms of entanglement thermodynamics.