dorsal/arxiv
View SchemaQuantum states and generalized observables: a simple proof of Gleason's theorem
| Authors | P. Busch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9909073 |
| URL | https://arxiv.org/abs/quant-ph/9909073 |
| DOI | 10.1103/PhysRevLett.91.120403 |
| Journal | Phys. Rev. Lett. 91, 120403 (2003) |
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.
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"abstract": "A quantum state can be understood in a loose sense as a map that assigns a\nvalue to every observable. Formalizing this characterization of states in terms\nof generalized probability distributions on the set of effects, we obtain a\nsimple proof of the result, analogous to Gleason\u0027s theorem, that any quantum\nstate is given by a density operator. As a corollary we obtain a von\nNeumann-type argument against non-contextual hidden variables. It follows that\non an individual interpretation of quantum mechanics, the values of effects are\nappropriately understood as propensities.",
"arxiv_id": "quant-ph/9909073",
"authors": [
"P. Busch"
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"quant-ph"
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"doi": "10.1103/PhysRevLett.91.120403",
"journal_ref": "Phys. Rev. Lett. 91, 120403 (2003)",
"title": "Quantum states and generalized observables: a simple proof of Gleason\u0027s theorem",
"url": "https://arxiv.org/abs/quant-ph/9909073"
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