Analysis for practical realization of number-state manipulation by number-sum Bell measurement with linear optics

We analyze the linear optical realization of number-sum Bell measurement and number-state manipulation by taking into account the realistic experimental situation, specifically imperfectness of single-photon detector. The present scheme for number-state manipulation is based on the number-sum Bell measurement, which is implemented with linear optical elements, i.e., beam splitters, phase shifters and zero-one-photon detectors. Squeezed vacuum states and coherent states are used as optical sources. The linear optical Bell state detector is formulated quantum theoretically with a probability operator measure. Then, the fidelity of manipulation and preparation of number-states, particularly for qubits and qutrits, is evaluated in terms of the quantum efficiency and dark count of single-photon detector. It is found that a high fidelity is achievable with small enough squeezing parameters and coherent state amplitudes.