On the role of the unitary transformations in Bell inequalities

Abstract: The role of the unitary transformations in the Bell-CHSH inequality is highlighted, in both Quantum Mechanics and relativistic Quantum Field Theory. In the former case, we discuss, through a few examples, how the violation of the Bell-CHSH inequality can be encoded into unitary transformations acting on a given reference set of Bell's observables. In the latter case, the Bell-CHSH inequality for a real massive scalar field in the vacuum state is considered. After introducing suitable bounded Hermitian operators, we show that using unitary transformations can significantly improve our previous numerical algorithm, leading to an increase in the size of the violation.