dorsal/arxiv
View SchemaDynamics of a quantum measurement
| Authors | Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412045 |
| URL | https://arxiv.org/abs/quant-ph/0412045 |
| DOI | 10.1016/j.physe.2005.05.023 |
Abstract
We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the apparatus is macroscopic. This implies to treat it with quantum statistical mechanics. The relevant time scales of the process are exhibited. It begins with a very rapid disappearance of the off-diagonal blocks of the overall density matrix of the tested system and the apparatus. Possible recurrences are hindered by the large size of the latter. On a much larger time scale the apparatus registers the outcome: Correlations are established between the final values of the pointer and the initial diagonal blocks of the density matrix of the tested system. We thus derive Born's rule and von Neumann's reduction of the state from the dynamical process.
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"abstract": "We work out an exactly solvable hamiltonian model which retains all the\nfeatures of realistic quantum measurements. In order to use an interaction\nprocess involving a system and an apparatus as a measurement, it is necessary\nthat the apparatus is macroscopic. This implies to treat it with quantum\nstatistical mechanics. The relevant time scales of the process are exhibited.\nIt begins with a very rapid disappearance of the off-diagonal blocks of the\noverall density matrix of the tested system and the apparatus. Possible\nrecurrences are hindered by the large size of the latter. On a much larger time\nscale the apparatus registers the outcome: Correlations are established between\nthe final values of the pointer and the initial diagonal blocks of the density\nmatrix of the tested system. We thus derive Born\u0027s rule and von Neumann\u0027s\nreduction of the state from the dynamical process.",
"arxiv_id": "quant-ph/0412045",
"authors": [
"Armen E. Allahverdyan",
"Roger Balian",
"Theo M. Nieuwenhuizen"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1016/j.physe.2005.05.023",
"title": "Dynamics of a quantum measurement",
"url": "https://arxiv.org/abs/quant-ph/0412045"
},
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