dorsal/arxiv
View SchemaNumerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior
| Authors | A. Månsson, P. G. L. Porta Mana, G. Björk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701087 |
| URL | https://arxiv.org/abs/quant-ph/0701087 |
Abstract
This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.
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"abstract": "This paper offers examples of concrete numerical applications of Bayesian\nquantum-state assignment methods to a three-level quantum system. The\nstatistical operator assigned on the evidence of various measurement data and\nkinds of prior knowledge is computed partly analytically, partly through\nnumerical integration (in eight dimensions) on a computer. The measurement data\nconsist in the average of outcome values of N identical von Neumann projective\nmeasurements performed on N identically prepared three-level systems. In\nparticular the large-N limit will be considered. Three kinds of prior knowledge\nare used: one represented by a plausibility distribution constant in respect of\nthe convex structure of the set of statistical operators; another one\nrepresented by a prior studied by Slater, which has been proposed as the\nnatural measure on the set of statistical operators; the last prior is\nrepresented by a Gaussian-like distribution centred on a pure statistical\noperator, and thus reflecting a situation in which one has useful prior\nknowledge about the likely preparation of the system. The assigned statistical\noperators obtained with the first two kinds of priors are compared with the one\nobtained by Jaynes\u0027 maximum entropy method for the same measurement situation.\nIn the companion paper the case of measurement data consisting in absolute\nfrequencies is considered.",
"arxiv_id": "quant-ph/0701087",
"authors": [
"A. M\u00e5nsson",
"P. G. L. Porta Mana",
"G. Bj\u00f6rk"
],
"categories": [
"quant-ph"
],
"title": "Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior",
"url": "https://arxiv.org/abs/quant-ph/0701087"
},
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