Axioms for the category of Hilbert spaces

Chris Heunen; Andre Kornell

doi:10.1073/pnas.2117024119

Axioms for the category of Hilbert spaces

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programmes such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.

Original language	English
Article number	e2117024119
Number of pages	5
Journal	Proceedings of the National Academy of Sciences (PNAS)
Volume	119
Issue number	9
Early online date	25 Feb 2022
DOIs	https://doi.org/10.1073/pnas.2117024119
Publication status	Published - 25 Feb 2022

Keywords / Materials (for Non-textual outputs)

Hilbert space
monoidal category
colimit

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10.1073/pnas.2117024119Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND)

2109.07418v2Accepted author manuscript, 353 KBLicence: All Rights Reserved
Axioms_HEUNEN_DOA18012022_VOR_CC-BY-NC-NDFinal published version, 827 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND)

https://www.pnas.org/doi/10.1073/pnas.2117024119Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND)

Combining Viewpoints in Quantum Theory (Ext.)
Heunen, C.
EPSRC
1/07/19 → 30/04/23
Project: Research

Cite this

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author = "Chris Heunen and Andre Kornell",

note = "Funding Information: ACKNOWLEDGMENTS. C.H. was supported by Engineering and Physical Sciences Research Council Fellowship EP/R044759/1. A.K. was supported by the Air Force Office of Scientific Research under Multidisciplinary University Research Initiative grant FA9550-16-1-0082. Publisher Copyright: {\textcopyright} 2022 National Academy of Sciences. All rights reserved.",

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AB - We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programmes such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.

KW - Hilbert space

KW - monoidal category

KW - colimit

U2 - 10.1073/pnas.2117024119

DO - 10.1073/pnas.2117024119

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JO - Proceedings of the National Academy of Sciences (PNAS)

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ER -

Axioms for the category of Hilbert spaces

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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Combining Viewpoints in Quantum Theory (Ext.)

Cite this