dorsal/arxiv
View SchemaHilbert-Schmidt Separability Probabilities and Noninformativity of Priors
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507203 |
| URL | https://arxiv.org/abs/quant-ph/0507203 |
| DOI | 10.1088/0305-4470/39/4/012 |
| Journal | J. Phys. A: Math. Gen. 39 (2006) 913-931 |
Abstract
The Horodecki family employed the Jaynes maximum-entropy principle, fitting the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We further extend the Horodecki one-parameter model in both these manners, obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for which we find a highly interesting/intricate continuum (-\infty < \alpha < \infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the golden ratio is featured. Our model can be contrasted with the three-parameter (b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a q(Tsallis)-parameter rather than $\alpha$, and has simply q-invariant HS separability probabilities of 1/2. Our results emerge in a study initially focused on embedding certain information metrics over the two-level quantum systems into a q-framework. We find evidence that Srednicki's recently-stated biasedness criterion for noninformative priors yields rankings of priors fully consistent with an information-theoretic test of Clarke, previously applied to quantum systems by Slater.
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"abstract": "The Horodecki family employed the Jaynes maximum-entropy principle, fitting\nthe mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by\nRajagopal by incorporating the dispersion (\\sigma_{1}^2) of the observable, and\nby Canosa and Rossignoli, by generalizing the observable (B_{\\alpha}). We\nfurther extend the Horodecki one-parameter model in both these manners,\nobtaining a three-parameter (b_{1},\\sigma_{1}^2,\\alpha) two-qubit model, for\nwhich we find a highly interesting/intricate continuum (-\\infty \u003c \\alpha \u003c\n\\infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the\ngolden ratio is featured. Our model can be contrasted with the three-parameter\n(b_{q}, \\sigma_{q}^2,q) one of Abe and Rajagopal, which employs a\nq(Tsallis)-parameter rather than $\\alpha$, and has simply q-invariant HS\nseparability probabilities of 1/2. Our results emerge in a study initially\nfocused on embedding certain information metrics over the two-level quantum\nsystems into a q-framework. We find evidence that Srednicki\u0027s recently-stated\nbiasedness criterion for noninformative priors yields rankings of priors fully\nconsistent with an information-theoretic test of Clarke, previously applied to\nquantum systems by Slater.",
"arxiv_id": "quant-ph/0507203",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/4/012",
"journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 913-931",
"title": "Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors",
"url": "https://arxiv.org/abs/quant-ph/0507203"
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