  We map the Hilbert space of the quantum Harmonic oscillator to the space of
Glauber's $n$th-order intensity correlators, in effect showing "the
correlations between the correlators" for a random sampling of the quantum
states. In particular, we show how the popular $g^{(2)}$ function is correlated
to the mean population and how a recurrent criterion to identify
single-particle states or emitters, namely $g^{(2)}<1/2$, is incorrect as
states exist that satisfy this condition with average population larger than
one. Our charting of the Hilbert space allows to capture its structure in a
simpler and physically more intuitive way that can be used to classify quantum
sources by surveying which territory they can access.
