Ontological models for quantum theory as functors

Alexandru Gheorghiu; Chris Heunen

doi:10.4204/EPTCS.318.12

Ontological models for quantum theory as functors

Alexandru Gheorghiu, Chris Heunen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract / Description of output

We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's result rules out functors that preserve a duality between states and measurement; Aaronson et al's result rules out functors that adhere to the Schrodinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.

Original language	English
Title of host publication	Proceedings 16th International Conference on Quantum Physics and Logic
Subtitle of host publication	Chapman University, Orange, CA, USA., 10-14 June 2019
Editors	Bob Coecke, Mathew Leifer
Publisher	Open Publishing Association
Pages	196-212
Number of pages	17
DOIs	https://doi.org/10.4204/EPTCS.318.12
Publication status	Published - 1 May 2020
Event	Quantum Physics and Logic 2019 - Orange, United States Duration: 10 Jun 2019 → 14 Jun 2019 https://qpl2019.org/

Publication series

Name	Electronic Proceedings in Theoretical Computer Science
Publisher	Open Publishing Association
Volume	318
ISSN (Electronic)	2075-2180

Conference

Conference	Quantum Physics and Logic 2019
Abbreviated title	QPL 2019
Country/Territory	United States
City	Orange
Period	10/06/19 → 14/06/19
Internet address	https://qpl2019.org/

Keywords / Materials (for Non-textual outputs)

quant-ph
math.CT

Access to Document

10.4204/EPTCS.318.12Licence: Creative Commons: Attribution (CC-BY)

1905.09055v1Accepted author manuscript, 1.21 MBLicence: Creative Commons: Attribution (CC-BY)
Ontological models_GHEORGHIU_DOA01052020_VOR_CC-BYFinal published version, 1.05 MBLicence: Creative Commons: Attribution (CC-BY)

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPL2019.12Licence: Creative Commons: Attribution (CC-BY)

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

Cite this

Gheorghiu, A., & Heunen, C. (2020). Ontological models for quantum theory as functors. In B. Coecke, & M. Leifer (Eds.), Proceedings 16th International Conference on Quantum Physics and Logic: Chapman University, Orange, CA, USA., 10-14 June 2019 (pp. 196-212). (Electronic Proceedings in Theoretical Computer Science; Vol. 318). Open Publishing Association. https://doi.org/10.4204/EPTCS.318.12

@inproceedings{9a438f94e8454745ae1f67a0b402a4c7,

title = "Ontological models for quantum theory as functors",

abstract = "We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's result rules out functors that preserve a duality between states and measurement; Aaronson et al's result rules out functors that adhere to the Schrodinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels. ",

keywords = "quant-ph, math.CT",

author = "Alexandru Gheorghiu and Chris Heunen",

note = "17 pages; Quantum Physics and Logic 2019, QPL 2019 ; Conference date: 10-06-2019 Through 14-06-2019",

year = "2020",

month = may,

day = "1",

doi = "10.4204/EPTCS.318.12",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science",

publisher = "Open Publishing Association",

pages = "196--212",

editor = "Bob Coecke and Mathew Leifer",

booktitle = "Proceedings 16th International Conference on Quantum Physics and Logic",

address = "Australia",

url = "https://qpl2019.org/",

}

Gheorghiu, A & Heunen, C 2020, Ontological models for quantum theory as functors. in B Coecke & M Leifer (eds), Proceedings 16th International Conference on Quantum Physics and Logic: Chapman University, Orange, CA, USA., 10-14 June 2019. Electronic Proceedings in Theoretical Computer Science, vol. 318, Open Publishing Association, pp. 196-212, Quantum Physics and Logic 2019, Orange, California, United States, 10/06/19. https://doi.org/10.4204/EPTCS.318.12

Ontological models for quantum theory as functors. / Gheorghiu, Alexandru; Heunen, Chris.
Proceedings 16th International Conference on Quantum Physics and Logic: Chapman University, Orange, CA, USA., 10-14 June 2019. ed. / Bob Coecke; Mathew Leifer. Open Publishing Association, 2020. p. 196-212 (Electronic Proceedings in Theoretical Computer Science; Vol. 318).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Ontological models for quantum theory as functors

AU - Gheorghiu, Alexandru

AU - Heunen, Chris

N1 - 17 pages

PY - 2020/5/1

Y1 - 2020/5/1

N2 - We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's result rules out functors that preserve a duality between states and measurement; Aaronson et al's result rules out functors that adhere to the Schrodinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.

AB - We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's result rules out functors that preserve a duality between states and measurement; Aaronson et al's result rules out functors that adhere to the Schrodinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.

KW - quant-ph

KW - math.CT

U2 - 10.4204/EPTCS.318.12

DO - 10.4204/EPTCS.318.12

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science

SP - 196

EP - 212

BT - Proceedings 16th International Conference on Quantum Physics and Logic

A2 - Coecke, Bob

A2 - Leifer, Mathew

PB - Open Publishing Association

T2 - Quantum Physics and Logic 2019

Y2 - 10 June 2019 through 14 June 2019

ER -

Gheorghiu A, Heunen C. Ontological models for quantum theory as functors. In Coecke B, Leifer M, editors, Proceedings 16th International Conference on Quantum Physics and Logic: Chapman University, Orange, CA, USA., 10-14 June 2019. Open Publishing Association. 2020. p. 196-212. (Electronic Proceedings in Theoretical Computer Science). Epub 2019 Jun 14. doi: 10.4204/EPTCS.318.12

Ontological models for quantum theory as functors

Abstract / Description of output

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Projects

Combining Viewpoints in Quantum Theory (Ext.)

Cite this