A New Light on Correlations for Multimode States

We present a new formalism for old intuition: the nth-order correlations in a multimode state are equivalent to the density matrix elements of the state formed by choosing
$n$
photons Ȝat randomȝ from the overall state and ignoring the rest. We develop expressions for choosing photons at random from a state. One photon randomly chosen will encode the state's intensity phenomena (like polarization), two will encode auto- and cross-correlation functions, and so on; this construction is unique and comprehensive.