Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse
Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse
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Abstract
Quantum mechanics and linguistics appear to be quite unrelated at first sight. Yet significant parts of both concern compositional reasoning about the way information flows among subsystems and the manner in which this flow gives rise to the properties of a system as a whole. This book is about the mathematics underlying this notion of compositionality, how it gives rise to intuitive diagrammatic calculi, and how these compositional methods are applied to reason about phenomena of both disciplines.Over the past decade, theoretical physics and quantum information theory have turned to category theory to model and reason about quantum protocols. This new use of categorical and algebraic tools allows a more conceptual and insightful expression of elementary events, such as measurements, teleportation, and entanglement operations, that were obscured in previous formalisms.Recent work in natural language semantics has begun to use these categorical methods to relate grammatical analysis and semantic representations in a unified framework for analyzing language meaning and learning meaning from a corpus. A growing body of literature on the use of categorical methods in quantum information theory and computational linguistics shows both the need and opportunity for new research on the relation between these categorical methods and the abstract notion of information flow.The aim of this book is to supply an overview of how categorical methods are used to model information flow in both physics and linguistics, to serve as an introduction to this interdisciplinary research, and to provide a basis for future research and collaboration between the different communities interested in applying category-theoretic methods to their domains’ open problems.
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Front Matter
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CHAPTER 1
CHAPTER 1 An Alternative Gospel of Structure: Order, Composition, Processes
Bob Coecke
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CHAPTER 2
Some Graphical Aspects of Frobenius Algebras
Fauser Bertfried
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CHAPTER 3
CHAPTER 3 A Graphical Approach to Measurement-BasedQuantum Computing
Ross Duncan
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CHAPTER 4
CHAPTER 4 Quantum Groups and Braided Algebra
Shahn Majid
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chapter-5
Hopf Algebras—Variant Notions and Reconstruction Theorems
Joost Vercruysse
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CHAPTER 6
CHAPTER 6 Modular Categories
MICHAEL MÜGER
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CHAPTER 7
CHAPTER 7 Scalars, Monads, and Categories
Dion Coumans andBart Jacobs
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CHAPTER 8
CHAPTER 8 Types and Forgetfulness in Categorical Linguistics and Quantum Mechanics
Peter Hines
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CHAPTER 9
From Sentence to Concept
Preller Anne
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CHAPTER 10
Proof Nets for the Lambek–Grishin Calculus
Moortgat Michael andMoot Richard
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CHAPTER 11
CHAPTER 11 Algebras over a Field and Semantics for Context-Based Reasoning
DAOUD CLARKE
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CHAPTER 12
CHAPTER 12 Distributional Semantic Models
Stephen Pulman
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CHAPTER 13
CHAPTER 13 Type-Driven Syntax and Semantics for Composing Meaning Vectors
STEPHEN CLARK
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End Matter
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