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 nontrivial manifestation of restricted quantum-classical correspondence. We demonstrate this observation by considering the full counting statistics which is associated with a two level coherent transition in the context of a continuous quantum measurement process. In particular we test the possibility of getting a valid result for var (Q) within the framework of the adiabatic picture, analyzing the simplest nontrivial example of a Landau-Zener crossing.