Dilation of states and processes in operational-probabilistic theories

Giulio Chiribella
(Institute for Interdisciplinary Information Sciences, Tsinghua University)

This paper provides a concise summary of the framework of operational-probabilistic theories, aimed at emphasizing the interaction between category-theoretic and probabilistic structures. Within this framework, we review an operational version of the GNS construction, expressed by the so-called purification principle, which under mild hypotheses leads to an operational version of Stinespring's theorem.

Invited Presentation 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. 1–14.
Published: 28th December 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.172.1 bibtex PDF
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