We propose a method to simulate a two-photon interference fringe by using a density matrix in order to describe various types of imperfections in the input state. Using this method, we numerically discuss the influence of various imperfections in an input state, such as dephasing and misalignment, on the quality (visibility and period) of the two-photon interference fringes. Applying this method to experimental data, we succeeded in numerically reproducing a two-photon interference fringe using the experimentally obtained density matrix, in which almost no free fitting parameters are required. From the results, because the main cause of the degradation of an interference fringe was found to be the limited aperture size of a two-photon detector, we can observe a two-photon interference fringe with a visibility of up to 94% in the experiments if an efficient two-photon absorbing material or a two-photon detector with a sufficiently high spatial resolution can be used.
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