V. BEHAVIOR OF A MEASUREMENT APPARATUS A. Non-classicality of a measurement ˆ Π$_{off}$ ( η, ν ) = e − ν ∞ ∑ n =0 (1 − η ) $^{n}$| n 〉〈 n | , (15) W [ n ] $_{cond}$( x, p ) = N ∫ dx $^{′}$dp$^{′}$W AB ( x, p ; x $^{′}$, p$^{′}$) W [ n ] $_{retr}$( x $^{′}$, p$^{′}$) , (14) We translate some interesting aspects of such a behavior in terms of pre-measurement states. This translation motivates the implementation of our experimental procedure for the tomography of these states, or the interpretation of results from realized experiments [4]. We also illustrate the relevance of these new properties for measurements on two well- known detectors from quantum optics: the Avalanche Photodiode (APD) and the Homodyne Detection (HD). There are different signatures for the non-classicality of states such as the negativity in particular quasi-probability distributions or the contextuality of hidden variable models trying to describe the measurement results [19, 20]. These two notions are in fact equivalent, as it was recently shown in Ref. [21]. The non-classicality of a measurement corresponds to the non-classicality of its pre- measurement state , for which such a notion is well-established with different signatures. We illustrate the relevance of such a correspondance for optical detectors in the condi- tional preparation of non-classical states of light. In such experiments [16, 17], we generally reconstruct from experimental data the Wigner representation of the conditioned state (10) given by: gaussian states, the necessary condition for preparing a non-classical state ˆ ρ [ n ] cond is to perform where W AB and W [ n ] retr are respectively the Wigner representations for the resource ˆ ρ$_{AB}$ and the pre-measurement state ˆ ρ [ n ] B, retr retrodicted from the expected result ’n’. N is a positive normalizing constant of W [ n ] $_{cond}$. When the resource has a non-negative representation as gaussian states, the necessary condition for preparing a non-classical state ˆ ρ [ n ] cond is to perform a non-classical measurement, in the sense of a non-positive Wigner representation W [ n ] $_{retr}$. In pratice, we use for such a task an Avalanche Photodiode (APD) which is a single- photon detector with only two responses, called ’off’ and ’on’. The response ’off’ corresponds to the imperfect detection of zero photon (see for example [22]): 11