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Article: Causality in Higher Order Process Theories

TitleCausality in Higher Order Process Theories
Authors
Issue Date18-Sep-2021
Citation
Electronic Proceedings in Theoretical Computer Science, 2021, v. 343, p. 265-300 How to Cite?
Abstract

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) [89]. 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.


Persistent Identifierhttp://hdl.handle.net/10722/340444
ISSN
2023 SCImago Journal Rankings: 0.370
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWilson, Matt-
dc.contributor.authorChiribella, Giulio-
dc.date.accessioned2024-03-11T10:44:42Z-
dc.date.available2024-03-11T10:44:42Z-
dc.date.issued2021-09-18-
dc.identifier.citationElectronic Proceedings in Theoretical Computer Science, 2021, v. 343, p. 265-300-
dc.identifier.issn2075-2180-
dc.identifier.urihttp://hdl.handle.net/10722/340444-
dc.description.abstract<p>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) [89]. 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.</p>-
dc.languageeng-
dc.relation.ispartofElectronic Proceedings in Theoretical Computer Science-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleCausality in Higher Order Process Theories-
dc.typeArticle-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.4204/EPTCS.343.12-
dc.identifier.scopuseid_2-s2.0-85115824733-
dc.identifier.volume343-
dc.identifier.spage265-
dc.identifier.epage300-
dc.identifier.isiWOS:001041743100012-
dc.identifier.issnl2075-2180-

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