dorsal/arxiv
View SchemaBayesian Thermostatistical Analyses of Two-Level Complex and Quaternionic Systems
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9710057 |
| URL | https://arxiv.org/abs/quant-ph/9710057 |
Abstract
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a quantum Fisher (Helstrom) information matrix. The square root of its determinant (adopting an ansatz of Harold Jeffreys) provides a reparameterization-invariant prior measure over the set. Both such measures can be properly normalized and their univariate marginal probability distributions (which serve as structure functions) obtained. Gibbs (posterior) probability distributions can then be found, using Poisson's integral representation of the modified spherical Bessel functions. The square roots of the (classical) Fisher information of these Gibbs distributions yield (unnormalized) priors over the inverse temperature parameters.
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"abstract": "The three and five-dimensional convex sets of two-level complex and\nquaternionic quantum systems are studied in the Bayesian thermostatistical\nframework introduced by Lavenda. Associated with a given parameterization of\neach such set is a quantum Fisher (Helstrom) information matrix. The square\nroot of its determinant (adopting an ansatz of Harold Jeffreys) provides a\nreparameterization-invariant prior measure over the set. Both such measures can\nbe properly normalized and their univariate marginal probability distributions\n(which serve as structure functions) obtained. Gibbs (posterior) probability\ndistributions can then be found, using Poisson\u0027s integral representation of the\nmodified spherical Bessel functions. The square roots of the (classical) Fisher\ninformation of these Gibbs distributions yield (unnormalized) priors over the\ninverse temperature parameters.",
"arxiv_id": "quant-ph/9710057",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"title": "Bayesian Thermostatistical Analyses of Two-Level Complex and Quaternionic Systems",
"url": "https://arxiv.org/abs/quant-ph/9710057"
},
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