COMPARATIVE NONINFORMATIVITIES OF QUANTUM PRIORS BASED ON MONOTONE METRICS

We consider a number of prior probability distributions of particular interest, all being defined on the three-dimensional convex set of two -level quantum systems. Each distribution is - following recent work o f Pert and Sudar - taken to be proportional to the volume element of a monotone metric on that Riemannian manifold. We apply an entropy-base d test (a variant of one recently developed by Clarke) to determine wh ich of two priors is more noninformative in nature. This involves conv erting them to posterior probability distributions based on some set o f hypothesized outcomes of measurements of the quantum system in quest ion. It is, then, ascertained whether or not the relative entropy (Kul lback-Leibler statistic) between a pair of priors increases or decreas es when one of them is exchanged with its corresponding posterior. The findings lead us to assert that the maximal monotone metric yields th e most noninformative prior distribution and the minimal monotone (tha t is, the Bures) metric, the least. Our conclusions both agree and dis agree, in certain respects, with ones recently reached by Hall, who re lied upon a less specific test criterion than our entropy-based one. ( C) 1998 Published by Elsevier Science B.V.