  The main focus of this thesis is to study the nonclassical and phase
properties of a family of engineered quantum states, most of which show various
nonclassical features. The beauty of these states is that these states can be
used to establish quantum supremacy. Earlier, a considerable amount of works
has been reported on various types of quantum states and their nonclassical
properties. Here, complementing the earlier works, the effect of
non-Gaussianity inducing operators on the nonclassical and phase properties of
displaced Fock states have been studied. This thesis includes 6 chapters. In
Chapter 1, motivation behind performing the present work is stated explicitly,
also the basic concepts of quantum optics are discussed with a specific
attention on the witnesses and measures of nonclassicality. In Chapter 2,
nonclassical properties of photon added and subtracted displaced Fock states
have been studied using various witnesses of lower- and higher-order
nonclassicality which are introduced in Chapter 1. In Chapter 3, we have
continued our investigation on photon added and subtracted displaced Fock
states (and their limiting cases). In this chapter, quantum phase properties of
these states are investigated from a number of perspectives, and it is shown
that the quantum phase properties are dependent on the quantum state
engineering operations performed. In Chapter 4, we have continued our
investigation on the impact of non-Gaussianity inducing operators on the
nonclassical and phase properties of the displaced Fock states. In Chapter 5,
we have performed a comparison between to process that are used in quantum
state engineering to induce nonclassical features. Finally, this thesis is
concluded in Chapter 6, where we have summarized the findings of this thesis
and have also described scope of the future works.
