Quantum to classical transition via fuzzy measurements on high gain spontaneous parametric down-conversion

We consider the high gain spontaneous parametric down-conversion in a non collinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of non-locality in an increasing size n/2-spin singlet state by studying the change in the correlations form as $n$ increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell's inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about 10^3. Our results enlighten the practical extreme difficulty of observing non-locality by performing such a dichotomic fuzzy measurement.