Noninformative Quantum q-Priors
| dc.creator | Slater, Paul B. | |
| dc.date | 2005-07-01 | |
| dc.date.accessioned | 2026-07-07T06:13:07Z | |
| dc.date.available | 2026-07-07T06:13:07Z | |
| dc.description | 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_{F_{q=1}} > p_{B} > p_{B_{q=1}trunc} >p_{F}) 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 p_{B} and p_{F} are the (independent-of-q) normalized volume elements of these metrics, and p_{F_{q=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_{B_{q=1}trunc}, 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. | |
| dc.description | 18 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0507014 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0507014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92993 | |
| dc.subject | Quantum Physics | |
| dc.title | Noninformative Quantum q-Priors | |
| dc.type | text |