A Protocol of Quantum Energy Distribution

Recently a remarkable quantum protocol, quantum energy tele-portation(QET) has been proposed, in which localized energy can be transported on average from one position to another only by LOCC. The protocol attains a cruicial propterty that dissipation of the energy transportation is drastically suppressed. This is because we transmit only classical information through a classical channel. The teleporta-tion is performed by use of ground-state entanglement of spin chain systems. In this paper, an extended protocol, quantum energy distribu-tion(QED) is proposed by combining QET and quantum key distribu-tion(QKD). In the protocol, multi-parties can simultaneously extract positive energy on average from spin chains by use of common secret key shared by the energy supplier. QED is robust against impersonation. An adversary, who does not have common secret key and tries to get energy, cannot obtain but give energy to the spin chains. Total amount of energy transfer gives a lower bound of residual energy of a local cooling process by the supplier. We also analyze an example of quantum energy distribution in the one-dimensional Ising model. Amount of distributed energy is evaluated depending on distance from the energy supplier.