Optical qubit by conditional interferometry

We suggest a method to prepare any chosen superposition $a_0|0〉{+a}_1|1〉$ of the vacuum and one-photon states. The method is based on a conditional double interferometer fed by a one-photon state and a coherent state. The scheme involves only linear optical elements and avalanche photodetectors, and therefore it should be realizable with current technology. A realistic description of the triggering photodetectors is employed, i.e., we assume that they can only check, with a certain efficiency, whether or not any photon is present. We discuss two working regimes, and show that output states with fidelity arbitrarily close to unit may be obtained, with nonvanishing conditional probability, also for low quantum efficiency at the photodetectors.