Determination of the phase-difference distribution between two weak optical fields

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Abstract
We reconsider the determination of the operational defined phase difference between two weak optical fields based on photon counting when the small number of possible experimental outcomes makes it harder to derive a continuous phase distribution. We show that the experimental procedure introduced to overcome this difficulty, namely, an external phase shifting of one input state, is not necessary. Indeed, all measuring data conditioned on the phase shift can be obtained from the data recorded without the external phase shift. Moreover, we investigate the effect of retaining ambiguous data or discarding even more data than only the ambiguous ones, respectively, and discuss the influence of a nonunit efficiency of the photodetectors.