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  1.  31
    Quantum Logic and Probability Theory.Alexander Wilce - 2008 - Stanford Encyclopedia of Philosophy.
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  2.  42
    Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories.Howard Barnum, Carl Philipp Gaebler & Alexander Wilce - 2013 - Foundations of Physics 43 (12):1411-1427.
    In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω B if, for any decomposition of ω B as a mixture ω B =∑ i p i β i of states β i on B, there exists an observable {a i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β i . This is always so for pure bipartite states in quantum mechanics, a fact (...)
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  3.  32
    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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  4.  41
    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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  5.  62
    Formalism and Interpretation in Quantum Theory.Alexander Wilce - 2010 - Foundations of Physics 40 (4):434-462.
    Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally (...)
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  6.  31
    Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models.Howard Barnum, Ross Duncan & Alexander Wilce - 2013 - Journal of Philosophical Logic 42 (3):501-523.
    In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete “operational” approach, in which the states and (...)
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  7.  19
    Introduction: Quantum Information Theory and Quantum Foundations.Howard Barnum, Stephanie Wehner & Alexander Wilce - 2018 - Foundations of Physics 48 (8):853-856.
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  8.  5
    A Royal Road to Quantum Mechanics.Alexander Wilce - unknown
    This paper fails to derive quantum mechanics from a few simple postulates. But it gets very close --- and it does so without much exertion. More exactly, I obtain a representation of finite-dimensional probabilistic systems in terms of euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together, and allows some --- but not too much --- room for more exotic alternatives.
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  9.  6
    Rob Clifton: Quantum Entanglements: Selected Papers, Edited by Jeremy Butterfield and Hans Halvorson. [REVIEW]Alexander Wilce - 2006 - Philosophy of Science 73 (1):122-124.