High-Temperature Expansions of Bures and Fisher Information Priors

Details High-Temperature Expansions of Bures and Fisher Information Priors High-Temperature Expansions of Bures and Fisher Information Priors

1999-10-27

arxiv.org/abs/quant-ph/9910113v2

Phys. Rev. E, 61 (2000) 6087

Physics

Quantum Physics

Six pages, LaTeX. The title has been shortened (and then further modified), at the suggestion of a colleague. Other minor chan

Scientific paper

10.1103/PhysRevE.61.6087

For certain infinite and finite-dimensional thermal systems, we obtain --- incorporating quantum-theoretic considerations into Bayesian thermostatistical investigations of Lavenda --- high-temperature expansions of priors over inverse temperature beta induced by volume elements ("quantum Jeffreys' priors) of Bures metrics. Similarly to Lavenda's results based on volume elements (Jeffreys' priors) of (classical) Fisher information metrics, we find that in the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys' rule for variables over [0,infinity], by being proportional to 1/beta, or to the Bayes-Laplace principle of insufficient reason, by being constant. Whether a system adheres to one rule or to the other appears to depend upon its number of degrees of freedom.

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