  Conventional coherent states (CSs) are defined in various ways. For example,
CS is defined as an infinite Poissonian expansion in Fock states, as displaced
vacuum state, or as an eigenket of annihilation operator. In the infinite
dimensional Hilbert space, these definitions are equivalent. However, these
definitions are not equivalent for the finite dimensional systems. In this
work, we present a comparative description of the lower- and higher-order
nonclassical properties of the finite dimensional CSs which are also referred
to as qudit CSs (QCSs). For the comparison, nonclassical properties of two
types of QCSs are used: (i) nonlinear QCS produced by applying a truncated
displacement operator on the vacuum and (ii) linear QCS produced by the
Poissonian expansion in Fock states of the CS truncated at (d-1)-photon Fock
state. The comparison is performed using a set of nonclassicality witnesses
(e.g., higher order antiubunching, higher order sub-Poissonian statistics,
higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set
of quantitative measures of nonclassicality (e.g., negativity potential,
concurrence potential and anticlassicality). The higher order nonclassicality
witness have found to reveal the existence of higher order nonclassical
properties of QCS for the first time.
