Constructor Theory as Process Theory

• URL: http://arxiv.org/abs/2401.05364v1
• Date: Thu, 14 Dec 2023 12:58:55 GMT
• Title: Constructor Theory as Process Theory
• Authors: Stefano Gogioso (Hashberg Ltd), Vincent Wang-Ma\'scianica (Quantinuum Ltd), Muhammad Hamza Waseem (Quantinuum Ltd), Carlo Maria Scandolo (University of Calgary), Bob Coecke (Quantinuum Ltd)
• Abstract summary: We show how to formulate fundamental notions of constructor theory within the canvas of process theory. We answer the question of how constructor theory relates to the broader body of process-theoretic literature.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories of physics in terms of the (im)possibility to implement certain abstract "tasks" by means of physical processes. Process theory, on the other hand, pursues analogous characterisation goals in terms of the compositional structure of said processes, concretely presented through the lens of (symmetric monoidal) category theory. In this work, we show how to formulate fundamental notions of constructor theory within the canvas of process theory. Specifically, we exploit the functorial interplay between the symmetric monoidal structure of the category of sets and relations, where the abstract tasks live, and that of symmetric monoidal categories from physics, where concrete processes can be found to implement said tasks. Through this, we answer the question of how constructor theory relates to the broader body of process-theoretic literature, and provide the impetus for future collaborative work between the fields.

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