Handbook Of Quantum Logic And Quantum Structures

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Handbook Of Quantum Logic And Quantum Structures

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Author : Kurt Engesser
language : en
Publisher: Elsevier
Release Date : 2009-06-16

Handbook Of Quantum Logic And Quantum Structures written by Kurt Engesser and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-16 with Mathematics categories.

Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, "The logic of quantum mechanics, quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic. - Authored by eminent scholars in the field - Material presented is of recent origin representing the frontier of the subject - Provides the most comprehensive and varied discussion of Quantum Mechanics available

Handbook Of Quantum Logic And

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Author : Kurt Engesser
language : en
Publisher: Elsevier Science Limited
Release Date : 2007

Handbook Of Quantum Logic And written by Kurt Engesser and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics? quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic - A comprehensive presentation of the theory, approaches and results in the field of quantum logic - Volume focuses on quantum structures

Quantum Measure Theory

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Author : Jan Hamhalter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-31

Quantum Measure Theory written by Jan Hamhalter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-31 with Mathematics categories.

This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

High Level Structures For Quantum Computing

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Author : Jaroslaw Miszczak
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

High Level Structures For Quantum Computing written by Jaroslaw Miszczak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.

This book is concerned with the models of quantum computation. Information processing based on the rules of quantum mechanics provides us with new opportunities for developing more efficient algorithms and protocols. However, to harness the power offered by quantum information processing it is essential to control the behavior of quantum mechanical objects in a precise manner. As this seems to be conceptually difficult at the level of quantum states and unitary gates, high-level quantum programming languages have been proposed for this purpose. The aim of this book is to provide an introduction to abstract models of computation used in quantum information theory. Starting from the abstract models of Turing machine and finite automata, we introduce the models of Boolean circuits and Random Access Machine and use them to present quantum programming techniques and quantum programming languages. Table of Contents: Introduction / Turing machines / Quantum Finite State Automata / Computational Circuits / Random Access Machines / Quantum Programming Environment / Quantum Programming Languages / Imperative quantum programming / Functional Quantum Programming / Outlook

Multiple Valued Logic

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Author : D. Michael Miller
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Multiple Valued Logic written by D. Michael Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.

Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram. Table of Contents: Multiple Valued Logic Applications / MVL Concepts and Algebra / Functional Representations / Reversible andQuantum Circuits / Quantum Multiple-Valued Decision Diagrams / Summary / Bibliography

Samson Abramsky On Logic And Structure In Computer Science And Beyond

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Author : Alessandra Palmigiano
language : en
Publisher: Springer Nature
Release Date : 2023-08-01

Samson Abramsky On Logic And Structure In Computer Science And Beyond written by Alessandra Palmigiano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-01 with Philosophy categories.

Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers.

Fundamental Mathematical Structures Of Quantum Theory

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Author : Valter Moretti
language : en
Publisher: Springer
Release Date : 2019-06-20

Fundamental Mathematical Structures Of Quantum Theory written by Valter Moretti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Science categories.

This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.

Logic Language Information And Computation

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Author : Leonid Libkin
language : en
Publisher: Springer
Release Date : 2013-08-15

Logic Language Information And Computation written by Leonid Libkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Mathematics categories.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 20th Workshop on Logic, Language, Information and Communication, WoLLIC 2013, held in Darmstadt, Germany, in August 2013. The 17 contributed papers presented together with 6 invited lectures were carefully reviewed and selected from 30 submissions. The scope of the workshop spans the theoretical and practical aspects of formal logic, computing and programming theory, and natural language and reasoning.

Nature Of Computation And Communication

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Author : Cong Vinh Phan
language : en
Publisher: Springer Nature
Release Date : 2023-03-23

Nature Of Computation And Communication written by Cong Vinh Phan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-23 with Computers categories.

This book constitutes the refereed post-conference proceedings of the 8th EAI International Conference on Nature of Computation and Communication, ICTCC 2022, held in Vinh Long, Vietnam, in October 27-28 2022. The 11 revised full papers presented were carefully selected from 32 submissions. The papers of ICTCC 2022 cover formal methods for self-adaptive systems and discuss natural approaches and techniques for natural computing systems and their applications.

Wigner Type Theorems For Hilbert Grassmannians

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Author : Mark Pankov
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-16

Wigner Type Theorems For Hilbert Grassmannians written by Mark Pankov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.

An accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.