2005/07/01 by Paul B. Slater, Slater, Paul B.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0507014
18 pages, 8 figures
arxiv created 2005/07/01 · arxiv updated 2009/12/01
We find, in an analysis involving four prior probabilities (p's), that the information-theoretic-based comparative noninformativity test devised by Clarke, and applied by Slater in a quantum setting, yields a ranking (p_Fq=1 > pB > p_Bq=1trunc >pF) fully consistent with Srednicki's recently-stated criterion for priors of ``biasedness to pure states''. Two of the priors are formed by extending certain metrics of quantum-theoretic interest from three- to four-dimensions -- by incorporating the q-parameter (nonextensivity/Tsallis index/escort parameter). The three-dimensional metrics are the Bures (minimal monotone) metric over the two-level quantum systems and the Fisher information metric over the corresponding family of Husimi distributions. The priors pB and pF are the (independent-of-q) normalized volume elements of these metrics, and p_Fq=1 is the normalized volume element of the q-extended Fisher information metric, with q set to 1. While originally intended to similarly be the q-extension of the Bures metric, with q then set to 1, the prior p_Bq=1trunc, actually entails the truncation of the only off-diagonal entry of the extended Bures metric tensor. Without this truncation, the q-extended Bures volume element is null, as is also the case in two other quantum scenarios we examine.