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  1. Probabilistic Theories with Purification.Giulio Chiribella, Giacomo Mauro D'Ariano & Paolo Perinotti - unknown
    We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses (...)
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  • Local Tomography and the Jordan Structure of Quantum Theory.Howard Barnum & Alexander Wilce - 2014 - Foundations of Physics 44 (2):192-212.
    Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) (...)
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  • Four and a Half Axioms for Finite-Dimensional Quantum Probability.Alexander Wilce - 2012 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 281--298.
    It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, but as something closer to a probability calculus per se. However, from this angle, the rather special C *-algebraic apparatus of quantum probability theory stands in need of further motivation. One would like to find additional principles, having clear physical and/or probabilistic content, on the basis of which this apparatus (...)
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