Well, if you pick a particular state in the Hilbert space, it has a well-defined probability if it’s an eigenstate of the density matrix. This is an unusual operation that’s not usually talked about – because the density matrix isn’t an “observable” in the usual sense – like positions or momenta etc. But it’s still an operator on the Hilbert space. I will formally treat the density matrix rho as the “operator for the probability”.

— Density matrix and its classical counterpart

— Lubos Motl

2012.09.13 Thursday ACHK