  We precise for the first time the quantum behavior of a measurement apparatus
in the framework of the usual interpretation of quantum physics. We show how
such a behavior can also be studied by the retrodiction of pre-measurement
states corresponding to its responses. We translate in terms of these states
some interesting properties of the behavior of an apparatus, such as the
projectivity, the fidelity, the non-Gaussian character, or the non-classicality
of measurements performed by this one. We also propose an experimental
procedure allowing the tomography of these pre-measurement states for optical
detectors. We illustrate the relevance of these new notions for measurements,
by evaluating them for two detectors widely used in quantum optics: the
avalanche photodiode and the homodyne detection.
