Quantum Computation and Logic: How Quantum Computers Have Inspired Logical Investigations 1st ed. 2018 [Kõva köide]

  • Formaat: Hardback, 178 pages, kõrgus x laius: 235x155 mm, kaal: 465 g, 3 Illustrations, color; 15 Illustrations, black and white; XVI, 178 p. 18 illus., 3 illus. in color., 1 Hardback
  • Sari: Trends in Logic 48
  • Ilmumisaeg: 18-Dec-2018
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 303004470X
  • ISBN-13: 9783030044701
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  • Formaat: Hardback, 178 pages, kõrgus x laius: 235x155 mm, kaal: 465 g, 3 Illustrations, color; 15 Illustrations, black and white; XVI, 178 p. 18 illus., 3 illus. in color., 1 Hardback
  • Sari: Trends in Logic 48
  • Ilmumisaeg: 18-Dec-2018
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 303004470X
  • ISBN-13: 9783030044701

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.

Arvustused

"A very useful appendix is provided for the reader in order to clearly the notation and make the book easy reader and self-contained. I found the reading of this book extremely pleasant and insightful. ... the volume "Quantum Computation and Logic" represents a very deep approach for logical-foundational aspects of quantum computation and it is strongly promising for the next research." (H. Freytes, Studia Logica, Vol. 107, 2019)

1 The Mathematical Environment of Quantum Information
1(30)
1.1 Physics and Logic in Classical Information Theory
1(2)
1.2 From the Classical to the Quantum-Theoretic Formalism
3(2)
1.3 The Mathematics of Quantum Theory
5(11)
1.4 Composite Systems
16(3)
1.5 Time Evolution and Quantum Measurements
19(5)
1.6 The Unsharp Approaches to Quantum Theory
24(3)
1.7 Quantum Logics
27(2)
References
29(2)
2 Pieces of Quantum Information and Quantum Logical Gates
31(22)
2.1 Qubits, Quregisters and Mixtures of Quregisters
31(3)
2.2 Quantum Logical Gates
34(11)
2.3 Quantum Logical Circuits
45(2)
2.4 Physical Implementations by Optical Devices
47(5)
References
52(1)
3 Entanglement: Mystery and Resource
53(12)
3.1 Entangled Pure States
53(1)
3.2 The Einstein-Podolsky-Rosen Paradox
54(5)
3.3 Quantum Teleportation
59(4)
References
63(2)
4 From Quantum Circuits to Quantum Computational Logics
65(20)
4.1 A New Approach to Quantum Logic: Quantum Computational Logics
65(1)
4.2 A Sentential Quantum Computational Language
66(3)
4.3 A Holistic Computational Semantics
69(9)
4.4 Quantum Computational Logical Arguments
78(6)
References
84(1)
5 Individuals, Quantifiers and Epistemic Operators
85(32)
5.1 Introduction
85(1)
5.2 Truth-Perspectives
86(2)
5.3 A First-Order Epistemic Quantum Computational Language
88(3)
5.4 A Holistic Quantum Computational Semantics for a Fragment of the Language 1
91(4)
5.5 An Epistemic Quantum Computational Semantics
95(10)
5.6 Physical Examples and Relativistic-Like Epistemic Effects
105(7)
5.7 Quantifiers as Quantum Maps
112(4)
References
116(1)
6 From Qubits to Qudits
117(10)
6.1 Introduction
117(1)
6.2 Qudit-Spaces
118(2)
6.3 Quantum Logical Gates in Qudit-Spaces
120(4)
6.4 Lukasiewicz-Quantum Computational Logics
124(2)
References
126(1)
7 What Exactly Are Quantum Computations? Classical and Quantum Turing Machines
127(12)
7.1 Introduction
127(1)
7.2 Classical Deterministic and Probabilistic Machines
128(3)
7.3 Quantum State Machines
131(4)
7.4 Abstract Quantum Computing Machines
135(3)
References
138(1)
8 Ambiguity in Natural and Artistic Languages: A Quantum Semantic Analysis
139(12)
8.1 Introduction
139(1)
8.2 Vague Possible Worlds and Metaphors
140(2)
8.3 A Quantum Semantics for Musical Languages
142(7)
References
149(2)
9 Quantum Information in the Foundational and Philosophical Debates About Quantum Theory
151(12)
9.1 Information Interpretations of Quantum Theory
151(1)
9.2 The Collapse-Problems
152(1)
9.3 Determinism, Indeterminism, Realism
153(6)
9.4 A "Quantum Logical Thinking" in Different Fields
159(2)
References
161(2)
10 Mathematical Survey
163(12)
10.1 Introduction
163(1)
10.2 Algebraic Concepts
163(4)
10.3 Hilbert-Space Concepts
167(8)
Index 175
Maria Luisa Dalla Chiara, professor emeritus of Logic and Philosophy of Science at the University Florence is a past president of the "International Quantum Structures Association", of the "Italian Society of Logic and Philosophy of Science" and a past vice-president of the "Division of Logic, Methodology and Philosophy of Science". She is the author of books and articles concerning the following fields: quantum logic, quantum computation, foundations and philosophy of quantum theory, semantics of physical theories, theories of meaning, semantics of music. Roberto Giuntini, professor of Logic and Philosophy of Science at the University of Cagliari, is president of the "Italian Society of Logic and Philosophy of Science" and past president of the "International Quantum Structures Association". His research centers around the logico-algebraic structures of quantum theory and quantum computation. In 1998 he was awarded the Birkhoff-von Neumann Prize. Roberto Leporini received an MSc degree cum laude in Computer Science in 1999 and a PhD in Computer Science in 2004, both from the University of Milan. Since 2005 he is an assistant professor at the University of Bergamo. His main research interests are: quantum computing, quantum optics, quantum computational structures and logic. He has published over 40 papers in international journals and holds a patent on the construction of quantum circuits. He is the president of the "International Quantum Structures Association". Giuseppe Sergioli received an MSc degree in Theoretical Physics at the University of Catania and a PhD in Logic and Philosophy of Science at the University of Cagliari, where he is now an assistant professor. His main research interests are: quantum computing, quantum computational structures and quantum computational logics. He is the author of several papers published in prominent journals in the areas of physics, logic, foundations of physics and computer science.

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