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Probabilistic theories: What is special about quantum mechanics?

In Alisa Bokulich & Gregg Jaeger (eds.), Philosophy of Quantum Information and Entanglement. Cambridge University Press (2010)

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  1. Embedding Quantum Mechanics Into a Broader Noncontextual Theory.Claudio Garola & Marco Persano - 2014 - Foundations of Science 19 (3):217-239.
    Scholars concerned with the foundations of quantum mechanics (QM) usually think that contextuality (hence nonobjectivity of physical properties, which implies numerous problems and paradoxes) is an unavoidable feature of QM which directly follows from the mathematical apparatus of QM. Based on some previous papers on this issue, we criticize this view and supply a new informal presentation of the extended semantic realism (ESR) model which embodies the formalism of QM into a broader mathematical formalism and reinterprets quantum probabilities as conditional (...)
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  • Information Invariance and Quantum Probabilities.Časlav Brukner & Anton Zeilinger - 2009 - Foundations of Physics 39 (7):677-689.
    We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as (...)
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  • 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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