Causality in Higher Order Process Theories

Matt Wilson
Giulio Chiribella

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.

In Chris Heunen and Miriam Backens: Proceedings 18th International Conference on Quantum Physics and Logic (QPL 2021), Gdansk, Poland, and online, 7-11 June 2021, Electronic Proceedings in Theoretical Computer Science 343, pp. 265–300.
Published: 18th September 2021.

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