On quantum vs. classical probability

Physics – Quantum Physics

Scientific paper

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Major revision: key results unchanged, but derivation and discussion completely rewritten; 33 pages, no figures

Scientific paper

10.1016/j.aop.2009.09.013

Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry, probabilities, composition of systems, state preparation and reductionism. The essential distinction between classical and quantum theory, on the other hand, is shown to be joint decidability versus smoothness; for the latter in particular I supply ample explanation and motivation. Finally, I argue that beyond quantum theory there are no other generalisations of classical probability theory that are relevant to physics.

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