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.
Cite
@article{arxiv.quant-ph/9909073,
title = {Quantum states and generalized observables: a simple proof of Gleason's theorem},
author = {P. Busch},
journal= {arXiv preprint arXiv:quant-ph/9909073},
year = {2011}
}
Comments
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