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Link to original content: https://pubmed.ncbi.nlm.nih.gov/14525351
Quantum states and generalized observables: a simple proof of Gleason's theorem - PubMed Skip to main page content
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. 2003 Sep 19;91(12):120403.
doi: 10.1103/PhysRevLett.91.120403. Epub 2003 Sep 19.

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

P Busch  1
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Quantum states and generalized observables: a simple proof of Gleason's theorem

P Busch. Phys Rev Lett. .

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 noncontextual 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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