Title: Do we need to detect single photons to evidence interference of photon probability amplitudes?

Abstract: Subtracting accidental coincidences is a common practice quantum optics experiments. For zero mean Gaussian states, such as squeezed vacuum, we show that if one removes accidental coincidences the measurement results are quantitatively the same, both for photon coincidences at very low flux and for intensity covariances. Consequently, pure quantum effects at the photon level, like interference of photon wave functions or photon bunching, are reproduced in the correlation of fluctuations of macroscopic beams issued from spontaneous down conversion. This is true both in experiment if the detection resolution is smaller than the coherence cell (size of the mode), and in stochastic simulations based on sampling the Wigner function. We discuss the limitations of this correspondence, such as Bell inequalities (for which one cannot substract accidental coincidences), highly multimode situations such as quantum imaging, and higher order correlations.