Nijmegen Quantum Logic Group

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Categorical Quantum Mechanics I: Causal Quantum Processes

21 Oct 2015 [ arXiv ]

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. Classical and quantum systems are treated as distinct types, of which the respective behavioural properties are also specified in terms of processes and their compositions. In this first part of a two-part overview, 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, and we prove the no-signalling theorem. Notable contributions include new, elegant derivations of the no-broadcasting theorem, unitarity of evolution, and Stinespring dilation, all for any ‘quantum’ type in a general class of process theories.