In the last decades much attention has been attracted to the photon heralding technique [1], which consists in generating a photon pair in two modes and detecting a photon of one (idler) mode, preparing thus the other (signal) mode in a single-photon state. In this work we consider spontaneous parametric downconversion (SPDC) as a source of photon pairs and find the density matrix of the signal mode conditioned by a photon detection in the idler one. We take into account three physical parameters of the scheme: the degree of two-mode squeezing r produced by SPDC, the transmittance of the idler channel η, which includes the quantum efficiency of the photodetector, and the transmittance of the signal channel µ, see Fig. 1(a).

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