Dilation of states and processes in operational-probabilistic theories
نویسنده
چکیده
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 [12], which under mild hypotheses leads to an operational version of Stinespring’s theorem.
منابع مشابه
Performance Modeling of Power Generation System of a Thermal Plant
The present paper discusses the development of a performance model of power generation system of a thermal plant for performance evaluation using Markov technique and probabilistic approach. The study covers two areas: development of a predictive model and evaluation of performance with the help of developed model. The present system of thermal plant under study consists of four subsystems with...
متن کاملOperational Theories of Physics as Categories
We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with our new notion of an operational category. Our work is based on effectus theory, a recently developed area of categorical logic, to which we give an operationa...
متن کاملTesting axioms for quantum theory on probabilistic toy-theories
In D’Ariano in Philosophy of Quantum Information and Entanglement, Cambridge University Press, Cambridge, UK (2010), one of the authors proposed a set of operational postulates to be considered for axiomatizing Quantum Theory. The underlying idea is to derive Quantum Theory as the mathematical representation of a fair operational framework, i.e. a set of rules which allows the experimenter to m...
متن کاملStructure of Optimal State Discrimination in Generalized Probabilistic Theories
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that p...
متن کاملMathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant
The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability...
متن کامل