  In quantum optics, nonclassical properties of various quantum states of
radiation field are frequently studied. Some of those states are finite
dimensional and referred to as qudits. These states are important because of
their potential applications in quantum information processing. Further,
nonclassical states are those which do not have any classical counterpart.
Consequently, to establish quantum supremacy, we always require nonclassical
state. Recently, Sivakumar and Meher have studied the nonclassical properties
of the number state filtered coherent state, and shown that the number state
filtering introduces nonclassical features into coherent state which is
otherwise classical. This observation motivated us to investigate the role of
hole burning (state filtering) on a state which is already nonclassical.
Specifically, we have selected a Binomial state which is known to be
nonclassical as our test bed and burnt a hole at vacuum (equivalently filtered
the vacuum state). To check the nonclassical properties of vacuum filtered
binomial state, we have used Vogel's criterion, criterion of higher- and
lower-order antibunching, criterion of higher-order sub-Poissonian photon
statistics, Linear entropy etc. The investigation results show that vacuum
filtered binomial state studied here is highly nonclassical, and the hole
burning process enhances the nonclassical depth.
