Deterministic preparation of superpositions of vacuum plus one photon by adaptive homodyne detection: experimental considerations

The preparation stage of optical qubits is an essential task in all the experimental setups employed for the test and demonstration of quantum optics principles. We consider a deterministic protocol for the preparation of qubits as a superposition of vacuum and one photon number states, which has the advantage to reduce the amount of resources required via phase-sensitive measurements using a local oscillator ('dyne detection'). We investigate the performances of the protocol using different phase measurement schemes: homodyne, heterodyne, and adaptive dyne detection (involving a feedback loop). First, we define a suitable figure of merit for the prepared state and we obtain an analytical expression for that in terms of the phase measurement considered. Further, we study limitations that the phase measurement can exhibit, such as delay or limited resources in the feedback strategy. Finally, we evaluate the figure of merit of the protocol for different mode-shapes handily available in an experimental setup. We show that even in the presence of such limitations simple feedback algorithms can perform surprisingly well, outperforming the protocols when simple homodyne or heterodyne schemes are employed.