A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

Krzysztof  Bar; Jamie Vicary

doi:10.4204/EPTCS.172.23

A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

Krzysztof Bar, Jamie Vicary

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

Abstract

This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.

Original language	English
Title of host publication	Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014)
Editors	Bob Coecke, Ichiro Hasuo , Prakash Panangaden
Publisher	Open Publishing Association
Pages	316-322
DOIs	https://doi.org/10.4204/EPTCS.172.23
Publication status	Published - 28 Dec 2014
Event	11th workshop on Quantum Physics and Logic (QPL 2014) - Kyoto, Japan Duration: 4 Jun 2014 → 6 Jun 2014

Publication series

Name	Electronic Proceedings in Theoretical Computer Science
Publisher	Open Publishing Association
Volume	172
ISSN (Electronic)	2075-2180

Conference

Conference	11th workshop on Quantum Physics and Logic (QPL 2014)
Country/Territory	Japan
City	Kyoto
Period	4/06/14 → 6/06/14

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10.4204/EPTCS.172.23Licence: Creative Commons: Attribution (CC BY)

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPL2014.23.pdfLicence: Creative Commons: Attribution (CC BY)

Cite this

Bar, K., & Vicary, J. (2014). A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem. In B. Coecke, I. Hasuo , & P. Panangaden (Eds.), Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014) (pp. 316-322). (Electronic Proceedings in Theoretical Computer Science; Vol. 172). Open Publishing Association. https://doi.org/10.4204/EPTCS.172.23

Bar, Krzysztof ; Vicary, Jamie. / A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem. Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). editor / Bob Coecke ; Ichiro Hasuo ; Prakash Panangaden. Open Publishing Association, 2014. pp. 316-322 (Electronic Proceedings in Theoretical Computer Science).

@inproceedings{cf22360b7b944020aff520c56f6c4941,

title = "A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem",

abstract = "This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.",

author = "Krzysztof Bar and Jamie Vicary",

year = "2014",

month = dec,

day = "28",

doi = "10.4204/EPTCS.172.23",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science",

publisher = "Open Publishing Association",

pages = "316--322",

editor = "Bob Coecke and {Hasuo }, {Ichiro } and Panangaden, {Prakash }",

booktitle = "Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014)",

note = "11th workshop on Quantum Physics and Logic (QPL 2014) ; Conference date: 04-06-2014 Through 06-06-2014",

}

Bar, K & Vicary, J 2014, A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem. in B Coecke, I Hasuo & P Panangaden (eds), Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). Electronic Proceedings in Theoretical Computer Science, vol. 172, Open Publishing Association, pp. 316-322, 11th workshop on Quantum Physics and Logic (QPL 2014), Kyoto, Japan, 4/06/14. https://doi.org/10.4204/EPTCS.172.23

A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem. / Bar, Krzysztof ; Vicary, Jamie.
Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). ed. / Bob Coecke; Ichiro Hasuo ; Prakash Panangaden. Open Publishing Association, 2014. p. 316-322 (Electronic Proceedings in Theoretical Computer Science; Vol. 172).

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

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N2 - This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.

AB - This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.

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Bar K, Vicary J. A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem. In Coecke B, Hasuo I, Panangaden P, editors, Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014). Open Publishing Association. 2014. p. 316-322. (Electronic Proceedings in Theoretical Computer Science). doi: 10.4204/EPTCS.172.23

A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

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