dorsal/arxiv
View SchemaInsolubility of the Quantum Measurement Problem for Unsharp Observables
| Authors | P. Busch, A. Shimony |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9604013 |
| URL | https://arxiv.org/abs/quant-ph/9604013 |
| Journal | Stud. Hist. Phil. Mod. Phys. 27 (1996) 397-404. |
Abstract
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this problem by eliminating idealizations from the characterization of measurement. We state and prove two `insolubility theorems' that disappoint this hope. In both the initial state of the apparatus is taken to be mixed rather than pure, and the correlation of the object observable and the pointer observable is allowed to be imperfect. In the {\it insolubility theorem for sharp observables}, which is only a modest extension of previous results, the object observable is taken to be an arbitrary projection valued measure. In the {\it insolubility theorem for unsharp observables}, which is essentially new, the object observable is taken to be a positive operator v alued measure. Both theorems show that the measurement problem is not the consequence of neglecting the ever-present imperfections of actual measurements.
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"abstract": "The quantum mechanical measurement problem is the difficulty of dealing with\nthe indefiniteness of the pointer observable at the conclusion of a measurement\nprocess governed by unitary quantum dynamics. There has been hope to solve this\nproblem by eliminating idealizations from the characterization of measurement.\nWe state and prove two `insolubility theorems\u0027 that disappoint this hope. In\nboth the initial state of the apparatus is taken to be mixed rather than pure,\nand the correlation of the object observable and the pointer observable is\nallowed to be imperfect. In the {\\it insolubility theorem for sharp\nobservables}, which is only a modest extension of previous results, the object\nobservable is taken to be an arbitrary projection valued measure. In the {\\it\ninsolubility theorem for unsharp observables}, which is essentially new, the\nobject observable is taken to be a positive operator v alued measure. Both\ntheorems show that the measurement problem is not the consequence of neglecting\nthe ever-present imperfections of actual measurements.",
"arxiv_id": "quant-ph/9604013",
"authors": [
"P. Busch",
"A. Shimony"
],
"categories": [
"quant-ph"
],
"journal_ref": "Stud. Hist. Phil. Mod. Phys. 27 (1996) 397-404.",
"title": "Insolubility of the Quantum Measurement Problem for Unsharp Observables",
"url": "https://arxiv.org/abs/quant-ph/9604013"
},
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