  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.
