On quantum vs. classical probability
arXiv:0710.2119 · doi:10.1016/j.aop.2009.09.013
Abstract
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.
Major revision: key results unchanged, but derivation and discussion completely rewritten; 33 pages, no figures
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- Quantum-Bayesian Coherence
- Von Neumann Was Not a Quantum Bayesian
- Conjugates, Filters and Quantum Mechanics
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- Measurement-based quantum foundations
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- Local tomography and the Jordan structure of quantum theory
- Time Symmetry in Operational Theories
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- Reasoning about quantum systems at the macroscopic level