Year: 2021
Type: article
Abstract: Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key features of quantum supermaps were captured through a general categorical framework, which led to a framework of higher order process theories (HOPT). The HOPT framework models lower and higher order transformations in a single unified theory, with its mathematical structure shown to coincide with the notion of a closed symmetric monoidal category. Here we provide an equivalent construction of the HOPT framework from four simple axioms of process-theoretic nature. We then use the HOPT framework to establish connections between foundational features such as causality, determinism and signalling, alongside exploring their interaction with the mathematical structure of *-autonomy.
DOI: 10.4204/eptcs.343.12
Authors: Matt Wilson, Giulio Chiribella
Institution: University of Oxford
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funders: John Templeton Foundation, Innovation, Science and Economic Development Canada, Government of Canada, University College London, Croucher Foundation, Ontario Ministry of Research, Innovation and Science, Centre for Quantum Technologies, Institut Périmètre de physique théorique, Engineering and Physical Sciences Research Council, Ontario Ministry of Research and Innovation
OpenAlex ID: W3192977968