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Scott continuity is a concept from domain theory that had an unexpected previous life in the theory of von Neumann algebras. Scott-continuous states are known as normal states, and normal states are exactly the states coming from density matrices. Given this, and the usefulness of Scott continuity in domain theory, it is natural to ask whether this carries over to generalized probabilistic theories. We show that the answer is no - there are infinite-dimensional convex sets for which the set of Scott-continuous states on the corresponding set of 2-valued POVMs does not recover the original convex set, but is strictly larger. This shows the necessity of the use of topologies for state-effect duality in the general case, rather than purely order theoretic notions.
Information transfer in generalized probabilistic theories (GPT) is an important problem. We have dealt with the problem based on repeatability postulate, which generalizes Zureks result to the GPT framework [Phys. Lett. A textbf{379} (2015) 2694]. A
In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is in terms of the positivity of associated maps. The second relates
To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality o
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dy
Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it. This requires one to analyze the experimental data in a manner that does not presume the correctness of the quantum for