10 found
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  1.  64
    Three Slit Experiments and the Structure of Quantum Theory.Cozmin Ududec, Howard Barnum & Joseph Emerson - 2011 - Foundations of Physics 41 (3):396-405.
    In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is (...)
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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.  28
    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.  67
    The Many-Worlds Interpretation of Quantum Mechanics: Psychological Versus Physical Bases for the Multiplicity of "Worlds".Howard Barnum - unknown
    This unpublished 1990 preprint argues that a crucial distinction in discussions of the many-worlds interpretation of quantum mechanics (MWI) is that between versions of the interpretation positing a physical multiplicity of worlds, and those in which the multiplicity is merely psychological, and due to the splitting of consciousness upon interaction with amplified quantum superpositions. It is argued that Everett's original version of the MWI belongs to the latter class, and that most of the criticisms leveled against the MWI, in particular (...)
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  5.  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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  6.  96
    Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
    Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any such theory naturally (...)
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  7.  18
    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.  10
    Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
  9.  60
    Dieks' Realistic Interpretation of Quantum Mechanics: A Comment.Howard Barnum - unknown
    D. Dieks has proposed a semantical rule which he claims yields a realistic interpretation of the formalism of quantum mechanics without the projection postulate. I argue that his proposal is unacceptable because it violates a natural requirement of psychophysical parallelism. His "semantical rule" is not an acceptable interpretive rule because it does not identify structures in the theory with structures in our experience, but postulates a merely probabilistic relationship between the two. Dieks' interpretation is contrasted with Everett's relative state interpretation, (...)
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  10.  10
    Oracles and Query Lower Bounds in Generalised Probabilistic Theories.Howard Barnum, Ciarán M. Lee & John H. Selby - 2018 - Foundations of Physics 48 (8):954-981.
    We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality, purification, strong symmetry, and informationally consistent composition. Sorkin has (...)
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