Investigations on nonclassical effects such as revivals, squeezing and entanglement in quantum systems require, in general, knowledge of the state of the system as it evolves in time. The state (equivalently, the density matrix) is reconstructed from a tomogram obtained from experiments. A tomogram is a set of histograms of appropriately chosen observables. Reconstruction of the quantum state from a tomogram typically involves statistical procedures that could be cumbersome and inherently error-prone. It is therefore desirable to extract as much information as possible about the properties of the state directly from the tomogram. The theme of this thesis is the identification and quantification of nonclassical effects from appropriate tomograms. We have examined continuous-variable (CV) systems, hybrid quantum (HQ) systems and spin systems. The program is two-fold: (a) To compute tomograms of known states numerically at various instants during temporal evolution under specific Hamiltonians, and to examine their revival, squeezing and entanglement properties at these instants; (b) to compute tomograms from available experimental data, and to investigate their nonclassical features. The CV systems considered are primarily (i) a Bose-Einstein condensate (BEC) trapped in a double-well potential, and (ii) a radiation field interacting with a nonlinear multi-level atomic medium. The HQ systems considered are two-level atoms interacting with radiation fields. This allows for the possibility of examining both optical tomograms and qubit tomograms. Several initial states have been considered, including the standard coherent state (CS), the two-mode squeezed state, the binomial state, and states which display quantifiable departure from coherence, such as the photon-added coherent state and the boson-added coherent state.

Wave packet revival phenomena including full, fractional and super-revivals have been examined tomographically in the context of a single-mode field system and the bipartite BEC system. Squeezing properties such as quadrature, higher-order Hong-Mandel and Hillery-type squeezing, and entropic squeezing have been investigated in detail in CV systems by evaluating appropriate moments of observables, from tomograms. A major part of the thesis is devoted to a comparison between the performance of different entanglement indicators (computed from tomograms) that we have proposed.

We have also obtained and examined tomograms directly related to experiments reported in the literature. (i) We have analysed appropriate tomograms to distinguish between two 2-photon states produced in an experiment on a CV bipartite system. While photon coincidence count measurements were used for this purpose in the experiment, our investigation demonstrates that tomograms provide another powerful tool for examining differences between various quantum states. (ii) We have computed spin tomograms from data, obtained using liquid-state NMR techniques, from an experimental group. (iii) Equivalent circuits of multipartite HQ systems were provided by us to the IBM quantum computing platform. Based on these circuits, tomograms were generated by the platform by experiment as well as simulation. Corresponding tomograms were computed by us using the HQ model. The entanglement indicators calculated from these three sources of tomograms have been compared and contrasted.

The thesis highlights and elaborates upon the very useful and significant role played by tomograms in assessing nonclassical effects displayed by quantum systems, without resorting to detailed state reconstruction procedures.