We present the theory of fast electro-optic correlations when applied to quantized fields. We find that, contrary to standard spectrometry or Hanbury Brown and Twiss arrangements, which are inherently based on destructive detection, electro-optic correlations fulfill the conditions of quantum non-demolition measurements. This property allows most notably the measurement of first and second order correlation of the quantum vacuum, as well as single photons, in a time-domain scheme. We conclude with a proposal for experimental implementation inspired from cutting edge research.