  Combining techniques of cavity quantum electrodynamics, quantum measurement,
and quantum feedback, we have realized the heralded transfer of a polarization
qubit from a photon onto a single atom with 39% efficiency and 86% fidelity.
The reverse process, namely, qubit transfer from the atom onto a given photon,
is demonstrated with 88% fidelity and an estimated efficiency of up to 69%. In
contrast to previous work based on two-photon interference, our scheme is
robust against photon arrival-time jitter and achieves much higher
efficiencies. Thus, it constitutes a key step toward the implementation of a
long-distance quantum network.
