Quantum Information And Complexity

This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.

"The Winter School and the International Conference on 'Quantum Information and Complexity' was held from 6 to 10 January 2003, at Meijo University, Nagoya"--P. v.

Quantum information is a developing multi-disciplinary field, with many exciting links to white noise theory. This connection is explored and presented in this work, which effectively bridges the gap between quantum information theory and complex systems. Arising from the Meijo Winter School and International Conference, the lecture notes and research papers published in this timely volume will have a significant impact on the future development of the theories of quantum information and complexity. This book will be of interest to mathematicians, physicists, computer scientists as well as electrical engineers working in this field. Contents:Quantum Information, Quantum Communication and Innovation (L Accardi)On the Quantum Liouville Space (I Antoniou & Z Suchanecki)L1-Theory for the Kolmogorov Operators of Stochstic Generalized Burgers Equations (M Röckner & Z Sobol)Homogenization of Infinite Dimensional Diffusion Processes with Periodic Drift Coefficients (S Albeverio et al.)Some Topics on White Noise Analysis (T Hida & Si Si)On a Design of Transition Probabilities and Estimates of Cover Times (S Ikeda et al.)Recent Progress on the White Noise Approach to the Lévy Laplacian (H-H Kuo)An Infinite Dimensional Stochastic Process and the Lévy Laplacian Acting on WND-Valued Functions (K Nishi & K Saitô)Note on Poisson Noise (Si Si)Note on Linear Process (Win Win Htay)and other papers Readership: Researchers in probability and statistics and quantum information. Keywords:Quantum Information;Complexity;White Noise Theory;Levy Laplacian;Infinite Dimensional Stochastic Processes

Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity. The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area. The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.

Quantum Proofs provides an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, it discusses non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.