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

Krzysztof Bar
(Department of Computer Science, University of Oxford)
Jamie Vicary
(Department of Computer Science, University of Oxford)

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.

In Bob Coecke, Ichiro Hasuo and Prakash Panangaden: Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014), Kyoto, Japan, 4-6th June 2014, Electronic Proceedings in Theoretical Computer Science 172, pp. 316–332.
Published: 28th December 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.172.23 bibtex PDF

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