Dilation of states and processes in operational-probabilistic theories
  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. 
Giulio Chiribella (Institute for Interdisciplinary Information   Sciences, Tsinghua University)
quant-ph cs.LO