Information thermodynamics for quantum energy teleportation

We examine a quantum energy teleportation protocol between remort partners Alice an Bob on one-dimensional quantum spin model. Bob can extract energy from the ground state of the model by the feedback unitary operation, where the extraction is activated by local energy injection by Alice's projective measurement and subsequent classical communication of the measurement result. We derive two formulae for the maximally extracted energy and the maximum of energy reduction at Bob's site. We find that the formula of energy reduction can be transformed into the second law of effective information thermodynamics. We also find that the feedback unitary operation commutes with the interaction between Bob's spin and the others when the extracted energy is maximized.