Abstract
Quantum information theory has emerged as one of the new frontiers of science and technology over the last few decades. Unlike classical information theory that deals with the classical bit, quantum information theory is centred around the concept of a qubit. In contrast to the classical bit that can either be a 0 or 1, the qubit exists in a superposition of both states at the same time. The importance of quantum resources is evident from the fact that are certain information processing tasks like teleportation which cannot be accomplished with only classical resources and even though there are certain tasks like secret sharing which have classical counterparts, their outputs are greatly enhance when the classical resources are combined with quantum resources. While quantum superposition and entanglement are wellestablished quantum resources, recently, significant research has been carried out to explore the possibility of quantum coherence as a resource for information processing applications.
This thesis is divided into four chapters. While the first two chapters deal with the fundamentals of quantum information theory and quantum coherence, the last two chapters primarily deal with the two research problems on quantum coherence. The first chapter serves as a revision of the important introductory concepts of quantum information theory, starting with the significance of the famous Stern-Gerlach experiment and the rise of randomness to mathematical formalism and postulates of quantum mechanics. Then, we explore the connection between randomness and lack of information and further explore how classical information is different from quantum information alongwith a brief overview of its corresponding measures. Finally, the chapter ends with a layout of widelyused quantum resources along with its utility in some of the famous information processing tasks.
The second chapter mainly deals with a brief synopsis on quantum coherence. At first, it discusses the formulation of resource theory of quantum coherence, which is followed by an introduction to the widely accepted framework of quantifying coherence and some of the popularly used coherence quantifiers. Finally, the chapter concludes with the application of coherence in the fields of quantum thermodynamics, quantum algorithms, interference phenomena and phase discrimination. The third chapter addresses the first research topic of the thesis : broadcasting of quantum coherence. As quantum coherence has recently emerged as a key candidate for use as a resource in various quantum information processing tasks, hence, it is of utmost importance to explore the possibility of creating a greater number of coherent states from an existing coherent pair. This process is known as broadcasting of coherence. This chapter starts with a brief discussion on the famous no-cloning theorem, followed by an overview of approximate cloning transformations. After that, the motivation behind broadcasting of coherence is explored along with an introduction to the definitions of optimal and non-optimal broadcasting. In both these definitions, the most general two-qubit state is taken as the input to the cloner, while the most incoherent states are used as blank states of the cloner. This chapter leads to two important results. Firstly, it has been proved
that while optimal broadcasting is not possible (for both local and non-local cloners), nonoptimal broadcasting cannot be ruled out. Secondly, in case of non-optimal broadcasting, the coherence introduced in the output states of the cloner will always be lesser than the initial coherence of the input state. Finally, three classes of mixed states, namely, the statistical mixture of the most coherent state (MCS) and the most incoherent state (MIS), the Wernerlike states (WLS) and the Bell-diagonal states (BDS), are taken up for obtaining their respective ranges of non-optimal broadcasting in terms of their corresponding input state parameters.
The fourth and final chapter deals with the second research topic of the thesis : some peculiar properties of robustness of coherence (ROC). Here, it has been shown that robustness of coherence, in contrast to many popular quantitative measures of quantum coherence derived from the resource theoretic framework of coherence, may be sub-additive for a specific class of multi-partite quantum states. Furthermore, this chapter also highlights how the subadditivity is affected by admixture with other classes of states for which ROC is superadditive. Moreover, it has been shown that pairs of quantum states may have different orderings with respect to relative entropy of coherence, l1-norm of coherence and ROC and the difference in ordering for coherence measures chosen pairwise has been numerically studied.