Violation of a tripartite Bell inequality by weak measurements

Non-locality is one of the most characteristic trait of Quantum Mechanics, and it is linked to the conceptually counter-intuitive ability of some objects (when adequately prepared) to instantaneously know about each other’s state, no matter how much space-separated they are. At the development stage of Quantum Mechanics, non-locality had been an argument of intense debate among scientists due to its consequences that seemed to contradict physicists common sense. The scientific debate on the argument faced a turning point with the publication in 1964 of the landmark paper by J. S. Bell "On the Einstein-Podolsky-Rosen Paradox", which ended the discussion whether or not non-locality was a true aspect of physical reality, raising it to one of the fundamental aspect of our comprehension of the physical world. The scientific interest for non-locality has recently substantially increased due to its striking applications in Quantum Information Theory. The major innovative traits of Quantum Information Theory, compared to Classical Information Theory, arise in fact from the usage of non-locality as a resource for information manipulation and transmission. The aim of this thesis is to investigate experimentally the non-local properties of a quantum system. This work is one of the first to prove that it is possible to share the non-local correlations of a two-photon entangled singlet state among three observers. The sharing of non-local correlations was possible through the employment of a weak measurement scheme, used to entangle the polarization degree of freedom of photons with a path degree of freedom used as ancilla for the weak measurement. In this thesis we briefly review all the theoretical tools necessary to understand the work (Quantum Mechanics, Optics, Quantum Optics) and we discuss in depth all the aspects of our work. We demonstrate theoretically how non-locality sharing is achievable, showing that it is possible to simultaneously violate two CHSH inequalities among three observers sharing a two-photon singlet state. We describe precisely our setup and its implementation. We finally present the obtained results, which confirm our theoretical model and expectations. The achievement of double violation and the realization of a simple weak measurement scheme may have important applications for Quantum Random Number Generation or for Quantum Key Distribution exploiting weak measurements.