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There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex, strongly monoidal, functorial embedding of the category of trace preserving completely positive maps into the category of quasi-stochastic matrices. This establishes quantum theory as a subcategory of quasi-stochastic processes. Such an embedding is induced by a choice of minimal informationally complete POVMs. We show that any two such embeddings are naturally isomorphic. The embedding preserves the dagger structure of the categories if and only if the POVMs are symmetric, giving a new use of SIC-POVMs, objects that are of foundational interest in the QBism community. We also study general convex embeddings of quantum theory and prove a dichotomy that such an embedding is either trivial or faithful.
We address quantum decision theory as a convenient framework to analyze process discrimination and estimation in qubit systems. In particular we discuss the following problems: i) how to discriminate whether or not a given unitary perturbation has be
Reggeon field theory (RFT), originally developed in the context of high energy diffraction scattering, has a much wider applicability, describing, for example, the universal critical behavior of stochastic population models as well as probabilistic g
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of this resource. Here we solve this question complete
A physical theory is called non-local when observers can produce instantaneous effects over distant systems. Non-local theories rely on two fundamental effects: local uncertainty relations and steering of physical states at a distance. In quantum mec
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