Introduction

The quantum-classical divide and the limitations of using classical tools to study quantum systems have received attention for several decades. We examine specific aspects of this broad theme, primarily using quantum optics as the platform for our investigation. In this introductory chapter, we outline nonclassical effects such as wave packet revivals, squeezing and entanglement. We define several optical states, and give a pedagogical illustration of how these states differ in their dynamics. We then indicate two aspects studied in the sequel. First, the extraction of nonclassical properties directly from tomograms that are readily available from experiments, bypassing detailed state reconstruction. Tomograms, being probability distributions in contrast to the reconstructed Wigner functions, provide useful pointers to assess nonclassicality. Standard entanglement indicators defined using the density matrix are introduced, with reference to which we compare the performance of indicators obtained directly from optical and qubit tomograms. Second, we demonstrate the usefulness of applying time series and network analysis (originating from classical dynamical systems theory) to the dynamics of quantum observables.