Includes bibliographical references (pages 572-613) and index.
Contents:
Convexity, colours and statistics -- Geometry of probability distributions -- Much ado about spheres -- Complex projective spaces -- Outline of quantum mechanics -- Coherent states and group actions -- The stellar representation -- The space of density matrices -- Purification of mixed quantum states -- Quantum operations -- Duality : maps versus states -- Discrete structures in hilbert space -- Density matrices and entropies -- Distinguishability measures -- Monotone metrics and measures -- Quantum entanglement -- Multipartite entanglement -- Appendix A : Basic notions of differential geometry. -- Appendix B: Basic notions of group theory -- Appendix C: Geometry: do it yourself -- Appendix D: Hints and answers to the exercises.
Summary:
Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen-Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.