Abstract
The fifth lesson dealt with the precise description of quantum logic operations with trapped ions. We recalled the definition of phase and control-not gates and the link between them. We explained the principle of the Cirac and Zoller gate and its partial realization by the Boulder group, then its complete realization by the Innsbruck group. We showed how the operation of the gate could be analyzed in detail by so-called ion tomography operations. Finally, we describe a three-ion teleportation experiment carried out by the Innsbruck group.