Quantum states and generalized observables: a simple proof of Gleason's theorem
(May 2003)Abstract
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 non-contextual hidden variables. It follows that
on an individual interpretation of quantum mechanics, the values of effects are
appropriately understood as propensities.
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