Geometry of Quantum States

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 KochenSpecker 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.