A conditional scheme to prepare optical superposition of the vacuum and onephoton states using linear elements (beam splitters and phase-shifters) and avalanche photodetectors is suggested.
We suggest a method to prepare any chosen superposition a0∣0〉+a1∣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.
The work of Knill et. al. (2001) established the possibility of nondeterministic realization of certain quantum logic operations using linear optical elements, ancilla photons and postselection techniques.It was also shown that any discrete unitary operator acting on N optical modes can be implemented by a triangular multiport device constructed from a series of beam splitters and phase shifters (see work of Reck, Zeilinger et. al., 1994).Here, we consider the rectangular linear optical multiport that is used for the probabilistic realization of unitary transformations on n qubits.This kind of linear optical scheme is suitable for probabilistic realization of unitary operators using ancilla photons and projective measurements.Qubits are encoded into the bosonic states of optical modes in two possible polarizations, and a number of ancilla photons and photodetectors are used for postselection of the qubits' state, based on the output of the detectors.We derive a procedure of evolutionary operator calculation for schemes of the considered type and present algorithms for their efficient computation on symmetric state space.We also provide complexities for different algorithms for the computation of evolutionary operator and estimate demands of resources in each case.A destructive Toffoli gate, acting on three qubits, using one ancilla photon and a photodetector, is implemented using schemes of the presented type.