Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to define an uncountable infinitude of Riemannian (also monotone) metrics on the set of positive definite density matrices. We pose here the questions of what is the specific/unique Fisher information metric for the (classically-defined) Husimi distributions and how does it relate to the infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We find a highly proximate (small relative entropy) relationship between the probability distribution (the quantum Jeffreys' prior) that yields quantum universal data compression, and that which (following Clarke and Barron) gives its classical counterpart. We also investigate the Fisher information metrics corresponding to the escort Husimi, positive-P and certain Gaussian probability distributions, as well as, in some sense, the discrete Wigner pseudoprobability. The comparative noninformativity of prior probability distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005]) -- formed by normalizing the volume elements of the various information metrics, is also discussed in our context.Comment: 27 pages, 10 figures, slight revisions, to appear in J. Math. Phy

Extension of Information Geometry to Non-statistical Systems: Some Examples

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.Comment: 8 pages, to be published in the proceedings of GSI2015, Lecture Notes in Computer Science, Springe

Regularization as quantization in reducible representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a classical current. The scheme implies a modified but very physically looking Hamiltonian. We solve Heisenberg equations of motion and compute photon statistics. Poisson statistics naturally occurs and no infrared divergence is found even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincar\'e covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to R\'enyi's $\alpha$. It is shown that the ``Shannon limit" $\alpha\to 1$ plays here a role of correspondence principle with the standard regularized formalism.Comment: minor extensions, version submitted for publicatio

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_{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.Comment: 26 pages, 12 figure

Stretched Exponential Relaxation in the Biased Random Voter Model

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe

A large synoptic dataset of coastal in situ observations

Since the beginning of 2004 MUMM has performed a series of moorings in the Belgian Coastal Zone with a tripod or benthic lander, equipped with a series of oceanographic sensors. Current meters such as an Acous1c Doppler Profiler (ADP) and an Acoustic Doppler Velocimeter (ADV), a CT-­sensor capable of measuring temperature and salinity, op1cal (OBS) and acous1c backsca\er sensors (ADP and ADV) to measure suspended sediment concentra1on, a LISST 100 suspended par1cle sizer, a passive Cetacean monitoring device (C-­PoD) and a passive sampling device for chemical monitoring have ever since been moored for more than 1750 days. From autumn 2009 a permanent coastal observatory has been installed at MOW1, located to the west of the entrance to the Zeebrugge harbor. Other mooring sites include more offshore loca1ons, such as the Kwintebank, Gootebank, MOW0 and the offshore windmill farms and a very nearshore loca1on (Blankenberge)

Symptoms associated with victimization in patients with schizophrenia and related disorders

Background: Patients with psychoses have an increased risk of becoming victims of violence. Previous studies have suggested that higher symptom levels are associated with a raised risk of becoming a victim of physical violence. There has been, however, no evidence on the type of symptoms that are linked with an increased risk of recent victimization. Methods: Data was taken from two studies on involuntarily admitted patients, one national study in England and an international one in six other European countries. In the week following admission, trained interviewers asked patients whether they had been victims of physical violence in the year prior to admission, and assessed symptoms on the Brief Psychiatric Rating Scale (BPRS). Only patients with a diagnosis of schizophrenia or related disorders (ICD-10 F20–29) were included in the analysis which was conducted separately for the two samples. Symptom levels assessed on the BPRS subscales were tested as predictors of victimization. Univariable and multivariable logistic regression models were fitted to estimate adjusted odds ratios. Results: Data from 383 patients in the English sample and 543 patients in the European sample was analysed. Rates of victimization were 37.8% and 28.0% respectively. In multivariable models, the BPRS manic subscale was significantly associated with victimization in both samples. Conclusions: Higher levels of manic symptoms indicate a raised risk of being a victim of violence in involuntary patients with schizophrenia and related disorders. This might be explained by higher activity levels, impaired judgement or poorer self-control in patients with manic symptoms. Such symptoms should be specifically considered in risk assessments

Microscopic Foundation of Nonextensive Statistics

Combination of the Liouville equation with the q-averaged energy $U_q = _q$ leads to a microscopic framework for nonextensive q-thermodynamics. The resulting von Neumann equation is nonlinear: $i\dot\rho=[H,\rho^q]$. In spite of its nonlinearity the dynamics is consistent with linear quantum mechanics of pure states. The free energy $F_q=U_q-TS_q$ is a stability function for the dynamics. This implies that q-equilibrium states are dynamically stable. The (microscopic) evolution of $\rho$ is reversible for any q, but for $q\neq 1$ the corresponding macroscopic dynamics is irreversible.Comment: revte