Modern Quantum Theory

In the last few decades quantum theory has experienced an extensive revival owing to the rapid development of quantum information and quantum technologies. Based on a series of courses taught by the authors, the book takes the reader on a journey from the beginnings of quantum theory in the early twentieth century to the realm of quantum-information processing in the twenty-first. The central aim of this textbook, therefore, is to offer a detailed introduction toquantum theory that covers both physical and information-theoretic aspects, with a particular focus on the concept of entanglement and its characteristics, variants, and applications.Suitable for undergraduate students in physics and related subjects who encounter quantum mechanics for the first time, this book also serves as a resource for graduate students who want to engage with more advanced topics, offering a collection of derivations, proofs, technical methods, and references for graduate students and more experienced readers engaged with teaching and active research.The book is divided into three parts: Part I - QuantumMechanics, Part II - Entanglement and Non-Locality, and Part III - Advanced Topics in Modern Quantum Physics. Part I provides a modern view on quantum mechanics, a central topic of theoretical physics.Part II is dedicated to the foundations of quantum mechanics and entanglement: starting with density operators, hidden-variable theories, the Einstein-Podolsky-Rosen Paradox, and Bell Inequalities, but also touching upon philosophical questions, followed by a deeper study of entanglement-based quantum communication protocols like teleportation, before giving a detailed exposition of entanglement theory, including tools for the detection and quantification of entanglement. Part III is intendedas a collection of standalone chapters to supplement the contents of Parts I and II, covering more advanced topics such as classical and quantum entropies, quantum operations and measurements,decoherence, quantum metrology and quantum optics, and entanglement in particle physics.

Reinhold Bertlmann is a professor of physics at the University of Vienna. He studied technical physics at TU Wien and theoretical physics at the University of Vienna, obtaining his PhD in 1974. He then worked as a researcher in Vienna, at the JINR in Dubna, and at CERN. After his habilitation in theoretical physics in Vienna in 1981 he held visiting professorships in Marseille, at the University Paris-Sud and at the CNRS. From 1987 until his retirement in 2010 hewas university professor at the University of Vienna, where he still teaches. Nicolai Friis studied physics at the University of Vienna and completed his diploma thesis under Reinhold Bertlmann'ssupervision in 2010. He then went on to study at the University of Nottingham, obtaining his PhD in 2013. From 2013 to 2017 he worked as a postdoctoral researcher in Innsbruck at the Institute for Quantum Optics and Quantum Information (IQOQI) and at the University of Innsbruck. In 2017 he moved back to Vienna as a Senior Postdoc at IQOQI Vienna. After his habilitation in theoretical physics in 2022, he started working at the Institute of Atomic and Subatomic Physics of TU Wien. He is thewinner of the Václav Votruba Prize for best doctoral thesis in theoretical physics, awarded by the Doppler Institute for Mathematical Physics and Applied Mathematics in Prague, Czech Republic.

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