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Categories for the Working Philosopher$
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Elaine Landry

Print publication date: 2017

Print ISBN-13: 9780198748991

Published to Oxford Scholarship Online: January 2018

DOI: 10.1093/oso/9780198748991.001.0001

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Categorical Quantum Mechanics I: Causal Quantum Processes

Categorical Quantum Mechanics I: Causal Quantum Processes

(p.286) 12 Categorical Quantum Mechanics I: Causal Quantum Processes
Categories for the Working Philosopher

Bob Coecke

Aleks Kissinger

Oxford University Press

We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes, and their interactions. We first present a general theory of diagrams, and in particular, of string diagrams, and discuss why diagrams are a very natural starting point for developing scientific theories. Then we define process theories, and define a very general notion of quantum type. We show how our process ontology enables us to assert causality, that is, compatibility of quantum theory and relativity theory, prove the no-signalling theorem, provide a new elegant derivation of the no-broadcasting theorem, unitarity of evolution, and Stinespring dilation, all for any `quantum' type in a general class of process theories.

Keywords:   string diagrams, quantum process, causality, no-broadcasting

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