dorsal/arxiv
View SchemaNoninformative Quantum q-Priors
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507014 |
| URL | https://arxiv.org/abs/quant-ph/0507014 |
Abstract
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.
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"abstract": "We find, in an analysis involving four prior probabilities (p\u0027s), that the\ninformation-theoretic-based comparative noninformativity test devised by\nClarke, and applied by Slater in a quantum setting, yields a ranking\n(p_{F_{q=1}} \u003e p_{B} \u003e p_{B_{q=1}trunc} \u003ep_{F}) fully consistent with\nSrednicki\u0027s recently-stated criterion for priors of ``biasedness to pure\nstates\u0027\u0027. Two of the priors are formed by extending certain metrics of\nquantum-theoretic interest from three- to four-dimensions -- by incorporating\nthe q-parameter (nonextensivity/Tsallis index/escort parameter). The\nthree-dimensional metrics are the Bures (minimal monotone) metric over the\ntwo-level quantum systems and the Fisher information metric over the\ncorresponding family of Husimi distributions. The priors p_{B} and p_{F} are\nthe (independent-of-q) normalized volume elements of these metrics, and\np_{F_{q=1}} is the normalized volume element of the q-extended Fisher\ninformation metric, with q set to 1. While originally intended to similarly be\nthe q-extension of the Bures metric, with q then set to 1, the prior\np_{B_{q=1}trunc}, actually entails the truncation of the only off-diagonal\nentry of the extended Bures metric tensor. Without this truncation, the\nq-extended Bures volume element is null, as is also the case in two other\nquantum scenarios we examine.",
"arxiv_id": "quant-ph/0507014",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"title": "Noninformative Quantum q-Priors",
"url": "https://arxiv.org/abs/quant-ph/0507014"
},
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