Bayesian Thermostatistical Analyses of Two-Level Complex and Quaternionic Systems
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.
Cite
@article{arxiv.quant-ph/9710057,
title = {Bayesian Thermostatistical Analyses of Two-Level Complex and Quaternionic Systems},
author = {Paul B. Slater},
journal= {arXiv preprint arXiv:quant-ph/9710057},
year = {2007}
}
Comments
6 pages, LaTeX, 6 postscript figures. This paper was submitted (in a non-LaTeX form) for publication in Dec., 1995, but not accepted. I have recast it into LaTeX for wider availability, primarily because it appears to have anticipated the recently-presented "quantum canonical ensemble" of Brody and Hughston (quant-ph/9709048)