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arXiv · 2610.40448

Process matrices on generalised theories

Matt Wilson·James Hefford·Timothée Hoffreumon
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Abstract

We extend the process-matrix framework for defining indefinite causal orders to a broad class of generalised physical theories. We give a simple re-axiomatisation of spacetime contexts in terms of naturality over classical probes, which precisely captures non-contextual assignment together with compatibility with convexity and coarse-graining within local laboratories. Using this compositional perspective, we give a clean characterisation of theories in which abstract spacetime contexts admit a process-matrix representation, and we pin down the precise conditions (satisfied by classical theory, quantum theory, and a Boxworld-like theory) under which the supermap and process-matrix perspectives on higher-order processes coincide.

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Matt Wilson, James Hefford, Timothée Hoffreumon. 2026-10-29. Process matrices on generalised theories. https://arxiv.org/abs/2610.40448

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