This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operatio...

Quantum physics, which offers an explanation of the world on the smallest scale, has fundamental implications that pose a serious challenge to ordinary logic. Particularly counterintuitive is the notion of entanglement, which has been explored for the past 30 years and posits an ubiquitous randomness capable of manifesting itself simultaneously in more than one place.This amazing 'non-locality' is more than just an abstract curiosity or paradox: it has entirely down-to-earth applica...

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption....

The essays in this book look at the question of whether physics can be based on information, or – as John Wheeler phrased it – whether we can get “It from Bit”. They are based on the prize-winning essays submitted to the FQXi essay competition of the same name, which drew over 180 entries.The eighteen contributions address topics as diverse as quantum foundations, entropy conservation, nonlinear logic and countable spacetime. Together they provide stimulating reading for all physic...

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written...

This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible.A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and ...

This book constitutes the thoroughly refereed post-conference proceedings of the 6th Conference on Theory of Quantum Computation, Communication, and Cryptography, TQC 2011, held in Madrid, Spain, in May 2011. The 14 revised papers presented were carefully selected from numerous submissions. The papers present new and original research and cover a large range of topics in quantum computation, communication and cryptography, a new and interdisciplinary field at the intersection of computer s...

This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic r...

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last c...

This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds.It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to ma...

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilat...

This monograph gives a thorough treatment of the celebrated compositions of signature and encryption that allow for verifiability, that is, to efficiently prove properties about the encrypted data.This study is provided in the context of two cryptographic primitives: (1) designated confirmer signatures, an opaque signature which was introduced to control the proliferation of certified copies of documents, and (2) signcryption, a primitive that offers privacy and authenticity at onc...