Entangled coherent states and violations of Bell-CHSH inequalities

Three classes of entangled coherent states are employed to study the Bell-CHSH inequality. By using pseudospin operators in infinite dimensional Hilbert spaces, four dichotomic operators $(A,A^{\mathrm{\prime }},B,B^{\mathrm{\prime }})$ entering the inequality are constructed. For each class of coherent states, we compute the correlator $⟨\psi \mathrm{\mid }AB+A^{\mathrm{\prime }}B+A{B}^{\mathrm{\prime }}-A^{\mathrm{\prime }}{B}^{\mathrm{\prime }}\mathrm{\mid }\psi ⟩$, analyzing the set of parameters that leads to a Bell-CHSH inequality violation and, particularly, to the saturation of Tsirelson’s bound.