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:quant-ph/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
- E-Print:
- 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