Quantum states and generalized observables: a simple proof of Gleason's theorem

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.

3 pages, revtex. New title, and presentation substantially revised, focus now being on the characterization of probability measures on the set of effects rather than the question of hidden variables

References in corpus (4)

• Hidden Variables and the Two Theorems of John Bell
• Non-Contextual Hidden Variables and Physical Measurements
• Existential Contextuality and the Models of Meyer, Kent and Clifton
• Kochen-Specker Theorem for Finite Precision Spin One Measurements

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