Msc in Applied Mathematics
MSc in Applied Mathematics Title: Mathematical and Technological Aspects of Quantum Information Processing Author: Jordi Tura i Brugués Advisor: Sebastià Xambó i Descamps Co-Advisor: Antonio Acín dal Maschio Department: Departament de Matemàtica Aplicada II Academic year: 2010-2011 Universitat Polit`ecnicade Catalunya Facultat de Matem`atiquesi Estad´ıstica Master's Degree Thesis Mathematical and Technological Aspects of Quantum Information Processing Jordi Tura i Brugu´es Advisor: Sebasti`aXamb´oi Descamps Co-Advisor: Antonio Ac´ındal Maschio Departament de Matem`aticaAplicada II Abstract Keywords: Quantum, information, processing, computation, coding, cryptography, entanglement, field theory, entropy, key distribution, protocols. Since its genesis, quantum mechanics has proved to be a very accurate model for predicting the behavior of the world below the nanoscale. However, crucial breakthroughs in technology were needed in order to be able to effectively access and manipulate such small magnitudes. During the last twenty years, the field of quantum information processing has experienced a growing interest, in its many variants, both theoretically and practically. Despite being still at a very basic stage, expectations are high. The uniqueness of quantum phenomena (superposition of states, creation of entanglement, etc.) have no classical analogue and allow novelties such as another paradigm of computation, more secure com- munications, quantum teleportation, quantum dense coding, etc. which are presented and analyzed here. The aim of this Thesis is to present in a unified way the main mathematical methods used in quantum information processing, as well as the state of the art of their corresponding technological implementa- tions. Our contributions are based in making a self-contained presentation; seeking completeness, that is, treating the most relevant fields of research involved, focusing on their relations; and picking the most relevant, insightful references, given the quantity of literature produced in this field.
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