Bennett and Stinespring, Together at Last

Chris Heunen; Robin Kaarsgaard

doi:10.4204/EPTCS.343

Bennett and Stinespring, Together at Last

Chris Heunen, Robin Kaarsgaard

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

Abstract / Description of output

We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the well-pointed restriction affine completion of a monoidal restriction category. This categorical completion encompasses both quantum channels, via Stinespring dilation, and classical computing, via Bennett's method. Moreover, in these two cases, we show how our construction can be 'undone' by a further universal construction. This shows how both mixed quantum theory and classical computation rest on entirely reversible foundations.

Original language	English
Title of host publication	Proceedings of the 18th International Conference on Quantum Physics and Logic (QPL 2021)
Publisher	EPTCS
Pages	102-118
Number of pages	17
DOIs	https://doi.org/10.4204/EPTCS.343
Publication status	Published - 18 Sept 2021
Event	18th International Conference on Quantum Physics and Logic - Gdańsk, Poland Duration: 7 Jun 2021 → 11 Jun 2021 https://qpl2021.eu/

Publication series

Name	Electronic Proceedings in Theoretical Computer Science, EPTCS
Publisher	Open Publishing Association
Number	343
ISSN (Electronic)	2075-2180

Conference

Conference	18th International Conference on Quantum Physics and Logic
Abbreviated title	QPL 2021
Country/Territory	Poland
City	Gdańsk
Period	7/06/21 → 11/06/21
Internet address	https://qpl2021.eu/

Keywords / Materials (for Non-textual outputs)

quant-ph
cs.LO
math.CT

Access to Document

10.4204/EPTCS.343Licence: Creative Commons: Attribution (CC-BY)

2102.08711v3Accepted author manuscript, 423 KBLicence: Creative Commons: Attribution (CC-BY)
Bennett and Stinespring_HEUNEN_DoA28052021_VOR_CC-BYFinal published version, 3.34 MBLicence: Creative Commons: Attribution (CC-BY)

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPL2021.5Licence: Creative Commons: Attribution (CC-BY)

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

Cite this

@inproceedings{a64eafe44eac4bcab7f98967315f8f55,

title = "Bennett and Stinespring, Together at Last",

abstract = "We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the well-pointed restriction affine completion of a monoidal restriction category. This categorical completion encompasses both quantum channels, via Stinespring dilation, and classical computing, via Bennett's method. Moreover, in these two cases, we show how our construction can be 'undone' by a further universal construction. This shows how both mixed quantum theory and classical computation rest on entirely reversible foundations. ",

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

author = "Chris Heunen and Robin Kaarsgaard",

note = "15 pages, additional proofs in appendix; 18th International Conference on Quantum Physics and Logic, QPL 2021 ; Conference date: 07-06-2021 Through 11-06-2021",

year = "2021",

month = sep,

day = "18",

doi = "10.4204/EPTCS.343",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science, EPTCS",

publisher = "EPTCS",

number = "343",

pages = "102--118",

booktitle = "Proceedings of the 18th International Conference on Quantum Physics and Logic (QPL 2021)",

url = "https://qpl2021.eu/",

}

Heunen, C & Kaarsgaard, R 2021, Bennett and Stinespring, Together at Last. in Proceedings of the 18th International Conference on Quantum Physics and Logic (QPL 2021). Electronic Proceedings in Theoretical Computer Science, EPTCS, no. 343, EPTCS, pp. 102-118, 18th International Conference on Quantum Physics and Logic, Gdańsk, Poland, 7/06/21. https://doi.org/10.4204/EPTCS.343

TY - GEN

T1 - Bennett and Stinespring, Together at Last

AU - Heunen, Chris

AU - Kaarsgaard, Robin

N1 - 15 pages, additional proofs in appendix

PY - 2021/9/18

Y1 - 2021/9/18

N2 - We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the well-pointed restriction affine completion of a monoidal restriction category. This categorical completion encompasses both quantum channels, via Stinespring dilation, and classical computing, via Bennett's method. Moreover, in these two cases, we show how our construction can be 'undone' by a further universal construction. This shows how both mixed quantum theory and classical computation rest on entirely reversible foundations.

AB - We present a universal construction that relates reversible dynamics on open systems to arbitrary dynamics on closed systems: the well-pointed restriction affine completion of a monoidal restriction category. This categorical completion encompasses both quantum channels, via Stinespring dilation, and classical computing, via Bennett's method. Moreover, in these two cases, we show how our construction can be 'undone' by a further universal construction. This shows how both mixed quantum theory and classical computation rest on entirely reversible foundations.

KW - quant-ph

KW - cs.LO

KW - math.CT

U2 - 10.4204/EPTCS.343

DO - 10.4204/EPTCS.343

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science, EPTCS

SP - 102

EP - 118

BT - Proceedings of the 18th International Conference on Quantum Physics and Logic (QPL 2021)

PB - EPTCS

T2 - 18th International Conference on Quantum Physics and Logic

Y2 - 7 June 2021 through 11 June 2021

ER -

Bennett and Stinespring, Together at Last

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