Even and odd trio coherent states: antibunching and violation of Cauchy$ndash$Schwarz inequalities

Even and odd trio coherent states are introduced by superposing two trio coherent states. Their antibunching and Cauchy–Schwarz inequalities are studied in detail. It is shown that, while odd trio coherent states are always antibunched and violate the Cauchy–Schwarz inequalities, even ones may or may not do so, depending on the parameters.