Quantum Computation and Logic: How Quantum Computers Have Inspired Logical Investigations (Trends in Logic)
By 作者: Maria Luisa Dalla Chiara – Roberto Giuntini – Roberto Leporini – Giuseppe Sergioli
ISBN-10 书号: 303004470X
ISBN-13 书号: 9783030044701
Edition 版本: 1st ed. 2018
出版日期: 2018-12-11
pages 页数: (192)

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.

Front Matter
1. The Mathematical Environment of Quantum Information
2. Pieces of Quantum Information and Quantum Logical Gates
3. Entanglement: Mystery and Resource
4. From Quantum Circuits to Quantum Computational Logics
5. Individuals, Quantifiers and Epistemic Operators
6. From Qubits to Qudits
7. What Exactly Are Quantum Computations? Classical and Quantum Turing Machines
8. Ambiguity in Natural and Artistic Languages:A Quantum Semantic Analysis
9. Quantum Information in the Foundational and Philosophical Debates About Quantum Theory
10. Mathematical Survey
Back Matter