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Abstract: Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The ensuing modifications affecting both classical and quantum bounds are elucidated. The relevance of a particular class of unitary operators whose expectation values are real is pointed out. For these operators, the classical and quantum bounds remain unaltered, being given, respectively, by $2$ and $2\sqrt{2}$. As an example, the Weyl unitary operators for a real scalar field in relativistic Quantum Field Theory are discussed.