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

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

1999-09-23

arxiv.org/abs/quant-ph/9909073v3

Phys. Rev. Lett. 91, 120403 (2003)

Physics

Quantum Physics

3 pages, revtex. New title, and presentation substantially revised, focus now being on the characterization of probability mea

Scientific paper

10.1103/PhysRevLett.91.120403

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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