The Study Of Quantum Information In High-Dimensional Hilbert Spaces

Quantum information theory is one of the newest research field that brings together disciplines of quantum mechanics and information science. Over the past decade, quantum information theory has developed into a significant and vigorous field of research.Recently, great interest has been absorbed to study quantum information in higher-dimensional Hilbert spaces. We also make a study in the field, we propose a linear optical scheme to implement Hogg's algorithm and probe into the domain of high-dimensional communication such as quantum cryptography and teleportation.The thesis consists of five chapters. In chapter one, we introduce the history of development and latest progress in the field of quantum computation and quantum information. In chapter two, we propose an efficient quantum computation scheme by encoding the quantum information in multi-photon coherent stateswe ang show that, using coherent quantum computation we can theoretically implement the highly structured search algorithm of three-qubit for 1-SAT problem proposed by Hogg. Chapter three we propose an extension of quantum key distribution based on encoding the key into quNits,i.e., a generalization of E91 quantum cryptography in a N-dimensional Hilbert space. In our protocol, we adopt asymmetric measurement scheme resulting in a higher efficiency and a generalized Bell inequality is employed to detect the presence of an eavesdropper Eve applying a cloning-based attack. General Schemes for teleportation in the case of high-dimension quantum states between two parties and multiparties is studied in chapter four.In chapter five a summary of the work and a outlook of this aspect are given.