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This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant approaches - perturbation theory and Feynman diagrammes, path integrals, and supergravity. The third chapter discusses the important concept of reparametrization invariance in the framework of simple systems: particle models, bosonic string, and parametrized field theory. This concept plays a crucial role in the Hamiltonian formulation of general relativity, which is the topic of Chapter 4. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while the sixth chapter presents loop quantum gravity. The next two chapters 7 and 8 then discuss the major applications - quantization of black holes and quantum cosmology. Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: the relevance of quantum gravity for the foundations of quantum theory and the arrow of time. It also contains a brief review of quantum-gravity phenomenology. The emphasis throughout is on conceptual and formal clarity. Wherever possible, connections between the various approaches are examined.

Quantum mechanics is a highly successful yet a mysterious theory. Quantum Mechanics for Beginners provides an introduction of this fascinating subject to someone with only a high school background in physics and mathematics. This book, except the last chapter on the Schrödinger equation, is entirely algebra-based. A major strength of this book is that, in addition to the foundation of quantum mechanics, it provides an introduction to the fields of quantum communication and quantum computing. The topics covered include wave–particle duality, the Heisenberg uncertainty relation, Bohr’s principle of complementarity, quantum superposition and entanglement, Schrödinger’s cat, Einstein–Podolsky–Rosen paradox, Bell theorem, quantum no-cloning theorem and quantum copying, quantum eraser and delayed choice, quantum teleportation, quantum key distribution protocols such as BB-84 and B-92, counterfactual communication, quantum money, quantum Fourier transform, quantum computing protocols including Shor and Grover algorithms, quantum dense coding, and quantum tunneling. All these topics and more are explained fully but using only elementary mathematics. Each chapter is followed by a short list of references and some exercises. This book is meant for an advanced high school student and a beginning college student and can be used as a text for a one semester course at the undergraduate level. However it can also be a useful and accessible book for those who are not familiar but want to learn some of the fascinating recent and ongoing developments in areas related to the foundations of quantum mechanics and its applications to quantum communication and quantum computing.

This book is a conceptual analysis of quantum information theory and the questions it raises for our understanding of the quantum world. Beginning from a detailed analysis of the concepts of information in the everyday and classical (Shannon) information-theory settings, an ontologically deflationary account of the nature of quantum information is developed. The account provided sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the process of quantum teleportation. In addition, it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. With a clear grasp of the concept of information in hand, attention turns to the pressing question whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. A number of common pitfalls are marked-out to be avoided before some concrete proposals are analysed in detail, including the radical quantum Bayesian programme of Caves, Fuchs and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had.

The Les Houches Summer School 2015 covered the emerging fields of cavity optomechanics and quantum nanomechanics. Optomechanics is flourishing and its concepts and techniques are now applied to a wide range of topics. Modern quantum optomechanics was born in the late 70s in the framework of gravitational wave interferometry, initially focusing on the quantum limits of displacement measurements. Carlton Caves, Vladimir Braginsky, and others realized that the sensitivity of the anticipated large-scale gravitational-wave interferometers (GWI) was fundamentally limited by the quantum fluctuations of the measurement laser beam. After tremendous experimental progress, the sensitivity of the upcoming next generation of GWI will effectively be limited by quantum noise. In this way, quantum-optomechanical effects will directly affect the operation of what is arguably the world’s most impressive precision experiment. However, optomechanics has also gained a life of its own with a focus on the quantum aspects of moving mirrors. Laser light can be used to cool mechanical resonators well below the temperature of their environment. After proof-of-principle demonstrations of this cooling in 2006, a number of systems were used as the field gradually merged with its condensed matter cousin (nanomechanical systems) to try to reach the mechanical quantum ground state, eventually demonstrated in 2010 by pure cryogenic techniques and a year later by a combination of cryogenic and radiation-pressure cooling. The book covers all aspects—historical, theoretical, experimental—of the field, with its applications to quantum measurement, foundations of quantum mechanics and quantum information. Essential reading for any researcher in the field.

Recent advances in quantum technology – from quantum computers and simulators to communication and metrology – have not only opened up a whole new world of applications but also changed the understanding of quantum theory itself. This text introduces quantum theory entirely from this new perspective. It does away with the traditional approach to quantum theory as a theory of microscopic matter, and focuses instead on quantum theory as a framework for information processing. Accordingly, the emphasis is on concepts like measurement, probability, statistical correlations, and transformations, rather than waves and particles. The text begins with experimental evidence that forces one to abandon the classical description and to re-examine such basic notions as measurement, probability, and state. Thorough investigation of these concepts leads to the alternative framework of quantum theory. The requisite mathematics is developed and linked to its operational meaning. This part of the text culminates in an exploration of some of the most vexing issues of quantum theory, regarding locality, non-contextuality, and realism. The second half of the text explains how the peculiar features of quantum theory are harnessed to tackle information processing tasks that are intractable or even impossible classically. It provides the tools for understanding and designing the pertinent protocols, and discusses a range of examples representative of current quantum technology.

This volume gathers the lectures notes of Session CVII of the Les Houches summer school of Physics, entitled “Current trends in Atomic Physics”. The school took place in July 2016 and had the goal to give the participants a broad overview of Atomic Physics as a whole, and in particular its connections to other areas of physics, such as condensed-matter and high-energy physics. The book comprises twelve chapters corresponding to lectures delivered at the school.

Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.