  It is demonstrated that the the statistics for a joint measurement of two
conjugate variables in Quantum Mechanics are expressed through an equation
identical to the classical one, provided that joint classical probabilities are
substituted by Wigner functions and that the interaction between system and
detectors is accounted for. This constitutes an extension of Ehrenfest
correspondence principle, and it is thereby dubbed strong correspondence
principle. Furthermore, it is proved that the detectors provide an additive
term to all the cumulants, and that if they are prepared in a Gaussian state
they only contribute to the first and second cumulant.
