Entanglement in Quantum Bit Cloning and in Hardy’s Paradox

Abstract

Quantum mechanics is the fundemental theory of all modern physics. As such it is a significant part of our understanding of Nature. It employs sophisticated mathematical models whose interpretation still poses unresolved physical and philosophical questions. Some of these lead to phenomena which are unusual and counterintuitive from an everyday perspective. In spite of this, quantum mechanics is a very successful theory. While its grounding fathers considered it as a theory for multipartite systems not verifyable on the level of individual physical systems, the formidable development of experimental technology (especially that of quantum optics) in the last decades has made the direct observation of these conterintuitive phenomena viable. And indeed: quantum mechanics appears to be valid for individual physical systems. Moreover, the accessibility of quantum phenomena seems to find its way to practical applications. The paradigm shift in physics introduced by quantum mechanics seems to be repeated in the field of information theory and information processing: quantum information now has a well-established reputation amongst future and emerging technologies. While quantum random generators and some quantum ciphers are commercial products already, yet there are still a lot of details to be better understood. The present dissertation describes my results which contribute mainly to the field of quantum information. In this field, quantum cloning is considered as an important information processing primitive. I have studied the interrelations of cloned quantum bits to a rest of the quantum system their originals belong to, in the case of a particular quantum cloner design. As quantum information science is often deeply related to the fundamental aspects of quantum mechanics. These aspects sometimes lead to paradoxical consequences when viewed from a classical physical perspective. My other aim was to better understand some details of such a paradox, introduced by Hardy. The dissertation itself is based on results which appeared in three independent publications. The topics may seem to be diverse, however, there is a key concept which interrelates all the presented results, namely quantum entanglement.