  We analyze the performance of a quantum repeater protocol based on single
trapped ions. At each node, single trapped ions embedded into high finesse
cavities emit single photons whose polarization is entangled with the ion
state. A specific detection of two photons at a central station located
half-way between two nodes heralds the entanglement of two remote ions.
Entanglement can be extended to long distances by applying successive
entanglement swapping operations based on two-ion gate operations that have
already been demonstrated experimentally with high precision. Our calculation
shows that the distribution rate of entanglement achievable with such an
ion-based quantum repeater protocol is higher by orders of magnitude than the
rates that are achievable with the best known schemes based on atomic ensemble
memories and linear optics. The main reason is that for trapped ions the
entanglement swapping operations are performed deterministically, in contrast
to success probabilities below 50 percent per swapping with linear optics. The
scheme requires efficient collection of the emitted photons, which can be
achieved with cavities, and efficient conversion of their wavelength, which can
be done via stimulated parametric down-conversion. We also suggest how to
realize temporal multiplexing, which offers additional significant speed-ups in
entanglement distribution, with trapped ions.
