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 vonNeumann 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.
 Publication:

Physical Review Letters
 Pub Date:
 September 2003
 DOI:
 10.1103/PhysRevLett.91.120403
 arXiv:
 arXiv:quantph/9909073
 Bibcode:
 2003PhRvL..91l0403B
 Keywords:

 03.65.Ca;
 03.65.Ta;
 03.67.a;
 Formalism;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum information;
 Quantum Physics
 EPrint:
 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