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

2003/09/19 by Paul Busch · 1 voice · 6 citations
Physics and Astronomy · Chemistry · Computer Science · #Quantum Mechanics and Applications #History and advancements in chemistry #Quantum Information and Cryptography

paper · doi:10.1103/physrevlett.91.120403

openalex publication_date 2003/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.

Citations

• On the Problem of Hidden Variables in Quantum Mechanics

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Discussions

• The Born rule is enunciated in many different forms, one possibility is Given a measurement represented by a POVM $\{F_j\}$ , the probability $p(j)$ of observing the outcome $j$ when making this measu [stackexchange, 1 points]

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