Quantum Energy Teleportation with Trapped Ions

We analyse a protocol of quantum energy teleportation that transports energy from the left edge of a linear ion crystal to the right edge by local operations and classical communication at a speed considerably greater than the speed of a phonon in the crystal. A probe qubit is strongly coupled with phonon fluctuation in the ground state for a short time, and it is projectively measured in order to obtain information about this phonon fluctuation. During the measurement process, phonons are excited by the time-dependent measurement interaction, and the energy of the excited phonons must be infused from outside the system. The obtained information is transferred to the right edge of the crystal through a classical channel. Even though the phonons excited at the left edge do not arrive at the right edge at the same time as when the information arrives at the right edge, we are able to soon extract energy from the ions at the right edge by using the transferred information. Because the intermediate ions of the crystal are not excited during the execution of the protocol, energy is transmitted in the energy transfer channel without heat generation.