Sharing nonlocality between sequential observers by means of projective measurements

Weak measurements are considered fundamental for sharing the nonlocality of an entangled two-qubit state between several sequential observers. In this thesis work, we show that this is not necessarily true. Indeed it is possible to share the nonlocality using only standard projective measurements, without the need for any quantum ancilla. We will first show that two sequential observers can both violate the CHSH inequality when the initial state is a maximally entangled two-qubit one and all the observers are allowed to share classical randomness. Afterward, we will determine the optimal trade-off relation between the CHSH parameters in the same scenario. We also show that two sequential violations can be reached without the need of sharing classical randomness, but using only projective measurements and local randomness. Secondly, we will study what happens if the initial state is non-maximally entangled and we will show that not only it is always possible to have two sequential violations with a partially entangled state, but that in some cases these states make larger sequential violations. Lastly, we prove that it is also possible for three sequential observers to violate the CHSH inequality. These results show that standard, projective, measurements are a simple and useful resource for sharing quantum nonlocality between sequential observers.