  Higher-order nonclassical properties of r photon added and t photon
subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are
investigated here to answer: How addition and subtraction of photon can be used
engineer higher-order nonclassical properties of qudit states? To obtain the
answer higher-order moment of relevant bosonic field operators are first
obtained for rPAQS and tPSQS, and subsequently the same is used to study the
higher-order nonclassical properties of the corresponding states. A few
witnesses of higher-order nonclassicality (e.g. Higher-Order Antibunching,
Higher-Order Squeezing of Hillery type, Higher-Order sub-Poissonian Photon
statistics) are first used to establish that rPAQS and tPSQS are highly
nonclassical. These witnesses are found to indicate that the amount of
nonclassicality enhances with the number of photon added (r). To quantitatively
establish this observation and to make a comparison between rPAQS and tPSQS,
volumes of the negative part of Wigner function (nonclassical volume) of rPAQS
and tPSQS are computed as a quantitative measure of nonclassicality. Finally,
for the sake of verifiablity of the obtained results, optical tomograms are
also reported which can be obtained experimentally and used to produce Wigner
function (which is not directly measurable in general) by the Radon transform.
Throughout the study, a particular type of qudit state named as a new
generalized binomial state is used as an example.
