  Individual atoms in optical cavities can provide an efficient interface
between stationary qubits and flying qubits (photons), which is an essentiel
building block for quantum communication. Furthermore, cavity assisted
controlled-not (CNOT) gates can be used for swapping entanglement to long
distances in a quantum repeater setup. Nonetheless, dissipation introduced by
the cavity during the CNOT may increase the experimental difficulty in
obtaining long-distance entanglement distribution using these systems. We
analyse and compare a number of cavity-based repeater schemes combining various
entanglement generation schemes and cavity assisted CNOT gates. We find that a
scheme, where high-fidelity entanglement is first generated in a two-photon
detection scheme and then swapped to long distances using a recently proposed
heralded CZ-gate exhibits superior performance compared to the other schemes.
The heralded gate moves the effect of dissipation from the fidelity to the
success probability of the gate thereby enabling high-fidelity entanglement
swapping. As a result, high-rate entanglement distribution can be achieved over
long distances even for low cooperativities of the atom-cavity systems. This
high-fidelity repeater is shown to outperform the other cavity-based schemes by
up to two orders of magnitude in the rate for realistic parameters and large
distances (1000 km).
