Restricted quantum-classical correspondence and counting statistics for a coherent transition

The conventional probabilistic point of view implies that if a particle has a probability p to make a transition from one site to another site, then the average transport should be 〈Q〉 = p with a variance Var(Q) = (1 − p)p. In the quantum mechanical context this observation becomes a non-trivial manifestation of restricted quantum-classical correspondence. We demonstrate this observation by considering the simplest non-trivial example: a two level Landau-Zener crossing in the adiabatic limit.