Quantum states and generalized observables: a simple proof of Gleason's theorem.
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple proof of the result, analogous to Gleason's theorem, that any quantum state is given by a density operator. As a corollary we obtain a von Neumann-type argument against noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.
Busch
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Department of Mathematics, University of Hull, Hull HU6 7RX, United Kingdom. p.busch@hull.ac.uk