Dagger and Dilation in the Category of Von Neumann algebras

2018/03/05 by Bas Westerbaan, Westerbaan, Bas
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Logic in Computer Science (cs.LO) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.1803.01911

openalex publication_date 2018/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This doctoral thesis is a mathematical study of quantum computing, concentrating on two related, but independent topics. First up are dilations, covered in chapter 2. In chapter 3 "diamond, andthen, dagger" we turn to the second topic: effectus theory. Both chapters, or rather parts, can be read separately and feature a comprehensive introduction of their own.

Citations

• Completely positive maps and entropy inequalities
• Effect algebras and unsharp quantum logics
• Operational Theories of Physics as Categories
• Subalgebras of C*-algebras
• Picture-perfect Quantum Key Distribution
• Quantum Computation and Quantum Information
• The Logic of Quantum Mechanics

Related

• Effectuses in Categorical Quantum Foundations
• Operator Algebras in Quantum Computation
• Theory of quantum computation
• A survey on algebraic dilatations
• Dagger Categories of Tame Relations