Misure deboli per la verifica di limiti locali e non-locali

The birth of Quantum Mechanics in the last century has brought with it a scientific revolution, both for fundamental research and technological applications in fields like communication, computation and metrology. This dissertation illustrates an experimental effort aiming at investigating the very foundations of this theory, as well as the problems connected to them. More specifically, we will address the measurement problem, connected to the interpretation of the wavefunction collapse, in the attempt to explain the interplay between the quantum and the classical description of physical reality. In this regard, classical theories, alternative to quantum mechanics, have been presented in the last century, e.g., the hidden variable theories (HVTs), so named as they depend on a set of hidden variables. These variables, completely inaccessible to any experimenter, would allow recovering the determinism of classical physics. In this perspective, the probabilistic nature of experimental results would be a consequence of the stochastic distribution of these hidden variables, i.e. Quantum Mechanics would be a statistical approximation of a classical theory. However, differences arise between Quantum Mechanics and HVTs when dealing, e.g., with entangled multi-partite systems, featuring correlations much stronger than any classical state and allowing to test the discrepancies between Quantum Mechanics and Local HVTs by violating the Bell Inequalities, always satisfied by these latter theories. One of them is the Clauser-Horne-Shimony-Holt (CHSH) inequality, indeed, violated by maximally-entangled states. Furthermore, stronger-than-quantum correlations have been discussed by S. Popescu and D. Rohrlich, introducing the so called PR-boxes. Within this debate, A. Carmi and E. Cohen introduced instead a principle called relativistic independence, stating that uncertainty relations should be intrinsically local, basically ruling out all non-local correlations beyond the quantum ones. The purpose of this work is studying these bounds for local and non-local correlations, some of them impossible to investigate with the usual quantum measurements, by exploiting a novel measurement paradigm called weak measurements: with a weak coupling between the examined system and the measurement device, it is possible to avoid the wave function collapse, inducing just a slight decoherence on the system state. This procedure grants unprecedented measurement capability, e.g., the possibility to measure non-commuting observables on the same quantum state, a key feature for our experiment. Specifically, we produce high-visibility polarization-entangled photon pairs within a Sagnac interferometer. The two photons are separated and collimated in a gaussian distribution, then each of them undergoes a sequence of two weak measurements before being detected by a spatial-resolving detector, that consists in an array of single-photon diodes, providing the possibility of estimating the correlations. With this setup, in the first instance we test the CHSH inequality in a totally novel way, i.e. without making its state to collapse after the weak measurement process. Second, we are able to measure in the weak regime, beside the CHSH value, also the correlations between subsequent measurements applied on the same particle, otherwise incompatible with each other. And, hence, we are able to explore the bound imposed to non-local correlations by the relativistic independence principle