PreprintCC BY 4.0arXiv
Process matrices on generalised theories
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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BibTeX
@misc{wilson2026process,
title = {{Process matrices on generalised theories}},
author = {Matt Wilson and James Hefford and Timothée Hoffreumon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40448},
eprint = {2610.40448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Process matrices on generalised theories
AU - Matt Wilson
AU - James Hefford
AU - Timothée Hoffreumon
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40448
UR - https://arxiv.org/abs/2610.40448
AB - 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.
ER -