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If losses were present (for example absorption), coupling with a vacuum operator would have to be introduced in order to preserve the unitary conditions. See: M.I. Kolobov, L.A. Lugiato, Phys. Rev. A 52, 4930 (1995). In this reference, this operator resulted from a finite pupil after the crystal and had no consequence on any normally-ordered correlation function. However, losses inside the crystal would imply a different situation, with actual parametric fluorescence generated from this introduced vacuum. This situation is outside the scope of the paper
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note
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r→,-r→ for intensities greater than 300 photons per pixel. This evolution confirms that quantum effects are more visible when thermal-like fluctuations are not too intense. It is not clear if the complete disappearance of quantum effects for high gains is physical or due to numerical accuracy problems. On the experimental side however, it is quite clear that the sub-shot noise level on the differences cannot be attained when the shot-noise fluctuations are very small compared to the thermal fluctuations
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