  We consider an experimentally obtainable SUP operator, defined by using a
generalized superposition of products of field annihilation ($a$) and creation
($a^\dagger$) operators of the type, $A = saa^\dagger+t{a^\dagger}a$ with
$s^2+t^2=1$. We apply this SUP operator on coherent and thermal quantum states,
the states thus produced are referred as SUP-operated coherent state (SOCS) and
SUP-operated thermal state (SOTS), respectively. In the present work, we report
a comparative study between the higher-order nonclassical properties of SOCS
and SOTS. The comparison is performed by using a set of nonclassicality
witnesses (e.g., higher-order antiubunching, higher-order sub-Poissonian photon
statistics, higher-order squeezing, Agarwal-Tara parameter, Klyshko's
condition). The existence of higher-order nonclassicalities in SOCS and SOTS
have been investigated for the first time. In view of possible experimental
verification of the proposed scheme, we present exact calculations to reveal
the effect of non-unit quantum efficiency of quantum detector on higher-order
nonclassicalities.
