2003/04/03 by Paul B. Slater, Slater, Paul B. · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0304029
nine pages, eight figures, LaTeX, some additional Commentary and analyses
openalex publication_date 2003/04/03 · arxiv created 2003/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the interrelationships between the Fisher information metric recently introduced, on the basis of maximum entropy considerations, by Brody and Hughston (quant-ph/9906085) and the monotone metrics, as explicated by Petz and Sudar. This new metric turns out to be not strictly monotone in nature, and to yield (via its normalized volume element) a prior probability distribution over the Bloch ball of two-level quantum systems that is less noninformative than those obtained from any of the monotone metrics, even the minimal monotone (Bures) metric. We best approximate the additional information contained in the Brody-Hughston prior over that contained in the Bures prior by constructing a certain Bures posterior probability distribution. This is proportional to the product of the Bures prior and a likelihood function based on four pairs of spin measurements oriented along the diagonal axes of an inscribed cube.