Dilation of states and processes in operational-probabilistic theories

Abstract

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.

arXiv commentIn Proceedings QPL 2014, arXiv:1412.8102

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• Consistency and Causality of Interconnected Nonsignaling Resources
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory