Hilbert-Schmidt separability probabilities and noninformativity of priors

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(2)(1)) 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(2)(1), alpha) two-qubit model, for which we find a highly interesting/intricate continuum (-infinity < a < infinity) 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(2)(q), q) one of Abe and Rajagopal, which employs a q(Tsallis)-parameter rather than a, 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, in this regard, 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.