Probing The Structure Of Quantum Mechanics: Nonlinearity, Nonlocality, Computation And Axiomatics

During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process).In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the fundamentals of quantum computation; and (2) a theoretical experimental part, which focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. Particular attention is also paid to the measurement problem, the classical limit and alternative interpretations (such as the hidden measurement approach).

Table of Contents:
Probing the Structure of Quantum Mechanics (D Aerts et al.); The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities (D Aerts & F Valckenborgh); Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities (D Aerts & F Valckenborgh); Being and Change: Foundations of a Realistic Operational Formalism (D Aerts); The Classical Limit of the Lattice-Theoretical Orthocomplementation in the Framework of the Hidden-Measurement Approach (T Durt & B D'Hooghe); State Property Systems and Closure Spaces: Extracting the Classical en Non-Classical Parts (D Aerts & D Deses); Hidden Measurements from Contextual Axiomatics (S Aerts); High Energy Approaches to Low Energy Phenomena in Astrophysics (S M Austin); Memory Effects in Atomic Interferometry: A Negative Result (T Durt et al.); Reality and Probability: Introducing a New Type of Probability Calculus (D Aerts); Quantum Computation: Towards the Construction of a 'Between Quantum and Classical Computer' (D Aerts & B D'Hooghe); Buckley-Siler Connectives for Quantum Logics of Fuzzy Sets (J Pykacz & B D'Hooghe); Some Notes on Aerts' Interpretation of the EPR-Paradox and the Violation of Bell-Inequalities (W Christiaens); Quantum Cryptographic Encryption in Three Complementary Bases Through a Mach-Zehnder Set Up (T Durt & B Nagler); Quantum Cryptography Without Quantum Uncertainties (T Durt); How to Construct Darboux-Invariant Equations of von Neumann Type (J L CieNli?ski); Darboux-Integrable Equations with Non-Abelian Nonlinearities (N V Ustinov & M Czachor); Dressing Chain Equations Associated with Difference Soliton Systems (S Leble); Covariance Approach to the Free Photon Field (M Kuna & J Naudts).