In their paper, Titulaer and Glauber state
The results [...] are derived only for fields with positive-definite P functions. Those are, in fact, precisely the quantum fields which may be described in a natural way as possessing classical analogs.
The $P$ function mentioned here is the Glauber-Sudarshan P representation. In the paper the authors shows that for $P \ge 0$ correlation functions follow a hierarchy of inequalities and, apparently, from these inequalities it follows that the state described by $P$ has a classical analog.
However, I fail to see how one can draw this conclusion, especially since this point is not further elucidated. So what is the argument I am missing or is there a better reference to see that positive $P$ functions correspond to classical states (or the often stated converse: negative $P$ indicate non classical behaviour)?
