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The past decade has seen a remarkable resurgence of the old programme of finding more or less a priori axioms for the mathematical framework of quantum mechanics.
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G. M. D’Ariano, Probabilistic theories: what is special about quantum mechanics? arXiv:0807.438v, 2008
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H. Barnum and A. Wilce, Information processing in convex operational theories, Proceedings of QPLV-DCMIV, Electronic Notes in Theoretical Computer Science (2008)
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