dorsal/arxiv
View SchemaNondemolition Principle of Quantum Measurement Theory
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512188 |
| URL | https://arxiv.org/abs/quant-ph/0512188 |
| DOI | 10.1007/BF02054669 |
| Journal | Foundations of Physics, 24 (1994) No 5, 685--714 |
Abstract
We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The "collapsed state-vector" after the "objectification" is simply treated as a random vector of the a posteriori state given by the quantum filtering, i.e., the conditioning of the a priori induced state on the corresponding reduced algebra. The nonlinear phenomenological equation of "continuous spontaneous localization" has been derived from the Schroedinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments.
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"abstract": "We give an explicit axiomatic formulation of the quantum measurement theory\nwhich is free of the projection postulate. It is based on the generalized\nnondemolition principle applicable also to the unsharp, continuous-spectrum and\ncontinuous-in-time observations. The \"collapsed state-vector\" after the\n\"objectification\" is simply treated as a random vector of the a posteriori\nstate given by the quantum filtering, i.e., the conditioning of the a priori\ninduced state on the corresponding reduced algebra. The nonlinear\nphenomenological equation of \"continuous spontaneous localization\" has been\nderived from the Schroedinger equation as a case of the quantum filtering\nequation for the diffusive nondemolition measurement. The quantum theory of\nmeasurement and filtering suggests also another type of the stochastic equation\nfor the dynamical theory of continuous reduction, corresponding to the counting\nnondemolition measurement, which is more relevant for the quantum experiments.",
"arxiv_id": "quant-ph/0512188",
"authors": [
"V. P. Belavkin"
],
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"quant-ph"
],
"doi": "10.1007/BF02054669",
"journal_ref": "Foundations of Physics, 24 (1994) No 5, 685--714",
"title": "Nondemolition Principle of Quantum Measurement Theory",
"url": "https://arxiv.org/abs/quant-ph/0512188"
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