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  1. Operational Axioms for Diagonalizing States.Giulio Chiribella & Carlo Maria Scandolo - 2015 - EPTCS 195:96-115.
    In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...)
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  • Infinitesimal Calculus as an Epistemic Mediator: A Commentary on the Use of Squares in Elementary Statistical Theory.Andrew Dynneson & Aaron Alvarez - unknown
    This is a commentary on the use of squares in elementary statistics. One sees an ubiquitous use of squares in statistics, and the analogy of "distance in a statistical sense" is teased out. We conjecture that elementary statistical theory has its roots in classical Calculus, and preserves the notion of two senses described in this paper. We claim that the senses of the differentials dx/dy hold between classical and modern infinitesimal Calculus and show how this sense becomes cashed out in (...)
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