ROLE OF MULTIPARTITE ENTANGLED STATES IN QUANTUM TELEPORTATION

Abstract

Quantum information science is a rapidly expanding field. Entanglement can be con sidered as heart of the quantum information theory. Although much research has been done on two-qubit entanglement, very little is known about multipartite entan glement. A better understanding of multipartite entanglement aids our understanding of the many-body system. There are many unanswered questions in the theory of multipartite systems. This is due to the complex structure of the multipartite system. The complexity of a multi-qubit system grows in proportion to the number of qubits and the dimension of the system. Entanglement is a quantum mechanical property that can be used as a resource in computational and communication tasks. It is es sential in many information processing protocols, including quantum cryptography, quantum superdense coding, and quantum teleportation. Although entangled states are useful in various quantum information processing tasks, the practical use of an entangled resource is restricted to the successful experimental realization of the re source. Non-locality is another quantum mechanical phenomenon which is not same as the entanglement. Although non-locality and quantum entanglement go hand in hand and they correspond to quantum correlation present in quantum states concep tually, they are very much distinct. At the level of a two-qubit entangled state and also for higher dimensional bipartite and multipartite entangled quantum states, it is possible to obtain more non-locality with less entanglement. Thus, we may expect that non-local states with less entanglement may be more useful as resource states. Many novel applications of non-locality have been developed for quantum computa tion and communication, including communication complexity, and quantum cryptog raphy. Quantum teleportation is an important topic to study in quantum information science. It plays a vital role in the development of quantum information theory and quantum technologies. Bennett et. al. have developed the first protocol of quantum teleportation for two-qubit system. By using quantum teleportation protocol, we can send information encoded in a quantum state in a more efficient way than the ex xiii isted classical protocols. The efficiency of the quantum teleportation protocol can be measured through the fidelity of a state known as teleportation fidelity. Another form of quantum teleportation is known as controlled quantum teleportation (CQT). CQT works perfectly for a three-qubit state shared between Alice, Bob and, Charlie where the third party Charlie acts as a controller. The importance of the CQT lies in the fact that in the CQT protocol, the controller has the power to enhance the teleportation fidelity of the two-qubit state possessed by Alice and Bob by performing measure ments on his qubit. Here, we have derived a different form of criteria, which is based on the maximum eigenvalue, for the detection of entangled state useful in quantum teleportation. The developed criterion may also be implementable in an experiment. Then, we have extensively studied the non-locality of the two-qubit state by defining a quantity that measures the strength of the non-locality. Later, we considered the three-qubit state (pure/mixed) and studied the non-locality of its reduced two-qubit state with the power of the controller of the three-qubit state in controlled quantum teleportation. Also, we have connected the non-locality of the three-qubit state with the non-locality of the two-qubit state by deriving the upper bound and lower bound of the Svetlichny operator. The derived state dependent bounds may be used to detect the genuine non-locality of any general three-qubit quantum state. Thus, the detection of genuine non-locality guarantees that the three-qubit state is genuinely entangled. At the end of the thesis, we studied the controlled quantum teleportation protocol us ing a three-qubit state and derived the lower bound of the controller’s power in terms of the introduced witness operator. Thus, our study may help to estimate the power of the controller in an experiment. Chapter 1 is introductory in nature. Chapters 2-5 are based on the research work published/communicated in the form of research papers in reputed journals. Finally, we conclude the thesis with future scope and references. Each chapter begins with a brief outline of the work carried out in that chapter.