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Quantum Computation and Logic

How Quantum Computers Have Inspired Logical Investigations

  • Maria Luisa Dalla Chiara
  • Roberto Giuntini
  • Roberto Leporini
  • Giuseppe Sergioli

Part of the Trends in Logic book series (TREN, volume 48)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 1-30
  3. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 31-52
  4. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 53-64
  5. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 65-84
  6. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 85-116
  7. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 117-126
  8. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 127-138
  9. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 139-150
  10. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 151-162
  11. Maria Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli
    Pages 163-174
  12. Back Matter
    Pages 175-178

About this book

Introduction

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

Keywords

Quantum Logics Non-Classical Logics Quantum Computation Quantum Gates Quantum Teleportation Quantum Computer Entanglement Epistemic Operators Quantum Information and Quantum Logical Gates Mathematical Environment of Quantum Information Quantum Entanglement Quantum Logical Circuits to Quantum Computational Logics Individuals, Quantifiers and Epistemic Operators Classical and Quantum Turing Machines Ambiguity in Natural and Artistic Languages

Authors and affiliations

  • Maria Luisa Dalla Chiara
    • 1
  • Roberto Giuntini
    • 2
  • Roberto Leporini
    • 3
  • Giuseppe Sergioli
    • 4
  1. 1.Department of PhilosophyUniversity of Florence FlorenceItaly
  2. 2.Department of PhilosophyUniversity of Cagliari CagliariItaly
  3. 3.Department of Management, Information and Production EngineeringUniversity of Bergamo Dalmine (Bergamo)Italy
  4. 4.Department of PhilosophyUniversity of Cagliari CagliariItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-04471-8
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-04470-1
  • Online ISBN 978-3-030-04471-8
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • Buy this book on publisher's site
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