# How did Glauber come up with his definition of non-classical states?

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)?

• You do appreciate "classical analog" states is a synonym for just generalized coherent states ("Schrodinger wave packets"), right? – Cosmas Zachos Apr 15 at 17:30
• @CosmasZachos I appreciate that this was new to me. Still, I fail to see that generalised coherent states necessarily produce positive P's and I still don't see the connection that is made in the paper, or more generally why Glauber defines "positive P are classical". – manthano Apr 16 at 5:08
• W Schleich’s textbook has a good review of this fact. – Cosmas Zachos Apr 16 at 10:45