  In quantum physics, the density operator completely describes the state.
Instead, in classical physics the mean value of every physical quantity is
evaluated by means of a probability distribution. We study the possibility to
describe pure quantum states and events with classical probability
distributions and conditional probabilities and prove that the distributions
can not be quadratic functions of the quantum state. Some examples are
considered. Finally, we deal with the exponential complexity problem of quantum
physics and introduce the concept of classical dimension for a quantum system.
