Higher-order CPM Constructions

Higher-order CPM Constructions

We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can be characterised by seeing the construction as an algebra for...

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Main Author: Stefano Gogioso
Format: Article
Language:English
Published: Open Publishing Association 2019-01-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1805.12079v2
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spelling doaj-eb766515b81044aaaf62421f4f5ee4e22020-11-25T01:15:32ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802019-01-01287Proc. QPL 201814516210.4204/EPTCS.287.8:60Higher-order CPM ConstructionsStefano Gogioso0 University of Oxford We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can be characterised by seeing the construction as an algebra for an appropriate monad. We provide several examples of the construction, connecting to previous work on the CPM construction and on categorical probabilistic theories, as well as upcoming work on higher-order interference and hyper-decoherence.http://arxiv.org/pdf/1805.12079v2
collection DOAJ
language English
format Article
sources DOAJ
author Stefano Gogioso
spellingShingle Stefano Gogioso
Higher-order CPM Constructions
Electronic Proceedings in Theoretical Computer Science
author_facet Stefano Gogioso
author_sort Stefano Gogioso
title Higher-order CPM Constructions
title_short Higher-order CPM Constructions
title_full Higher-order CPM Constructions
title_fullStr Higher-order CPM Constructions
title_full_unstemmed Higher-order CPM Constructions
title_sort higher-order cpm constructions
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2019-01-01
description We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can be characterised by seeing the construction as an algebra for an appropriate monad. We provide several examples of the construction, connecting to previous work on the CPM construction and on categorical probabilistic theories, as well as upcoming work on higher-order interference and hyper-decoherence.
url http://arxiv.org/pdf/1805.12079v2
work_keys_str_mv AT stefanogogioso higherordercpmconstructions
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