High-Temperature Expansions of Bures and Fisher Information Priors

Abstract

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.

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

References in corpus (3)

• Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
• On Bures fidelity of displaced squeezed thermal states
• A Comment on Fisher Information and Quantum Algorithms

Cited by in corpus (3)

• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors
• Essentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated