Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem

TY - JOUR

T1 - Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem

AU - Busch, Paul

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.91.120403

DO - 10.1103/PhysRevLett.91.120403

M3 - Article

SN - 0031-9007

VL - 91

SP - 1

EP - 4

JO - Physical Review Letters

JF - Physical Review Letters

IS - 12/120403

ER -