Dilation of states and processes in operational-probabilistic theories

TL;DR

This paper explores the framework of operational-probabilistic theories, highlighting the interplay between category theory and probability, and discusses an operational GNS construction and Stinespring's theorem.

Contribution

It introduces an operational perspective on the GNS construction and Stinespring's theorem within the framework of probabilistic theories, emphasizing categorical and probabilistic interactions.

Findings

Operational GNS construction via purification principle

Operational version of Stinespring's theorem derived

Framework unifies categorical and probabilistic structures

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.