Random quantum channels I: graphical calculus and the Bell state phenomenon

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an application, we study variations of random matrix models introduced by Hayden \cite{hayden}, and show that their eigenvalues converge almost surely. In particular we obtain for some models sharp improvements on the value of the largest eigenvalue, and this is shown in a further work to have new applications to minimal output entropy inequalities.Comment: Several typos were correcte

A Search for New Galactic Magnetars in Archival Chandra and XMM-Newton Observations

We present constraints on the number of Galactic magnetars, which we have established by searching for sources with periodic variability in 506 archival Chandra observations and 441 archival XMM-Newton observations of the Galactic plane (|b|<5 degree). Our search revealed four sources with periodic variability on time scales of 200-5000 s, all of which are probably accreting white dwarfs. We identify 7 of 12 known Galactic magnetars, but find no new examples with periods between 5 and 20 s. We convert this non-detection into limits on the total number of Galactic magnetars by computing the fraction of the young Galactic stellar population that was included in our survey. We find that easily-detectable magnetars, modeled after persistent anomalous X-ray pulsars, could have been identified in 5% of the Galactic spiral arms by mass. If we assume there are 3 previously-known examples within our random survey, then there are 59 (+92,-32) in the Galaxy. Transient magnetars in quiescence could have been identified throughout 0.4% of the spiral arms, and the lack of new examples implies that <540 exist in the Galaxy (90% confidence). Similar constraints are found by considering the detectability of transient magnetars in outburst by current and past X-ray missions. For assumed lifetimes of 1e4 yr, we find that the birth rate of magnetars could range between 0.003 and 0.06 per year. Therefore, the birth rate of magnetars is at least 10% of that for normal radio pulsars. The magnetar birth rate could exceed that of radio pulsars, unless the lifetimes of transient magnetars are >1e5 yr. Obtaining better constraints will require wide-field X-ray or radio searches for transient X-ray pulsars similar to XTE J1810--197, AX J1845.0--0250, CXOU J164710.2--455216, and 1E 1547.0-5408.Comment: 16 pages, 10 figures, one with a bit of color. submitted to Ap

Generating random density matrices

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi--partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N \to \infty, by the Marchenko-Pastur distribution.Comment: 13 pages in latex with 8 figures include

Random graph states, maximal flow and Fuss-Catalan distributions

For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated to a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.Comment: 37 pages, 24 figure

Random repeated quantum interactions and random invariant states

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}

Dry Bacterial Cellulose and Carboxymethyl Cellulose formulations with interfacial-active performance: processing conditions and redispersion

Dry or powdered formulations of food additives facilitate transportation, storage, preservation and handling. In this work, dry formulations of bacterial cellulose and carboxymethyl cellulose (BC:CMC), easily redispersible and preserving the functionality of the never-dried dispersions are reported. Different processing parameters and their effect on the materials properties were evaluated, namely: (i) wet-grinding of BC (Hand-blender, Microcut Head Impeller, High-pressure Homogenizer), (ii) drying of BC:CMC mixtures (fast drying at130 °C and slow drying at 80 °C) and subsequent (iii) comminution to different particle sizes. The dispersibility of the obtained BC:CMC powders was evaluated, and their functionality after redispersion was assessed by measuring the dynamic viscosity, the effect in oil/water interfacial tension (liquidliquid system) and the stabilization of cocoa in milk (solidliquid system). The size of BC fibre bundles was of paramount relevance to its stabilizing ability in multiphasic systems. A more extensive wet-grinding of the BC fibres was accompanied by a loss in the BC:CMC functionality, related to the increasingly smaller size of the BC bundles. Indeed, as the Dv (50) of the wet BC bundles was reduced from 1228 to 55 µm, the BC:CMC viscosity profile dropped and the effect on interfacial tension decreased. This effect was observed both on the never-dried and dry BC:CMC formulations. On the other hand, the drying method did not play a major effect in the materials properties. In a benchmarking study, the BC:CMC formulations, at a low concentration (0.15%), had better stabilizing ability of the cocoa particles than several commercial cellulose products.Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10570-020-03211-9) contains supplementary material, which is available to authorized users.This study was supported by FCT under the scope of the strategic funding of UID/BIO/04469/2019 unit and BioTecNorte operation (NORTE-01-0145-FEDER000004) funded by the European Regional Development Fund under the scope of Norte2020-Programa Operacional Regional do Norte. Daniela Martins also gratefully acknowledges FCT for the PhD scholarship, reference SFRH/BD/115917/2016.info:eu-repo/semantics/publishedVersio

Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values of all unit vectors in $V_n$ fills asymptotically (as $n$ tends to infinity) a deterministic convex set $K_{k,t}$ that we describe using a new norm in $\R^k$. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio

A review of exposure assessment methods for epidemiological studies of health effects related to industrially contaminated sites

BACKGROUND: this paper is based upon work from COST Action ICSHNet. Health risks related to living close to industrially contaminated sites (ICSs) are a public concern. Toxicology-based risk assessment of single contaminants is the main approach to assess health risks, but epidemiological studies which investigate the relationships between exposure and health directly in the affected population have contributed important evidence. Limitations in exposure assessment have substantially contributed to uncertainty about associations found in epidemiological studies. OBJECTIVES: to examine exposure assessment methods that have been used in epidemiological studies on ICSs and to provide recommendations for improved exposure assessment in epidemiological studies by comparing exposure assessment methods in epidemiological studies and risk assessments. METHODS: after defining the multi-media framework of exposure related to ICSs, we discussed selected multi-media models applied in Europe. We provided an overview of exposure assessment in 54 epidemiological studies from a systematic review of hazardous waste sites; a systematic review of 41 epidemiological studies on incinerators and 52 additional studies on ICSs and health identified for this review. RESULTS: we identified 10 multi-media models used in Europe primarily for risk assessment. Recent models incorporated estimation of internal biomarker levels. Predictions of the models differ particularly for the routes ‘indoor air inhalation’ and ‘vegetable consumption’. Virtually all of the 54 hazardous waste studies used proximity indicators of exposure, based on municipality or zip code of residence (28 studies) or distance to a contaminated site (25 studies). One study used human biomonitoring. In virtually all epidemiological studies, actual land use was ignored. In the 52 additional studies on contaminated sites, proximity indicators were applied in 39 studies, air pollution dispersion modelling in 6 studies, and human biomonitoring in 9 studies. Exposure assessment in epidemiological studies on incinerators included indicators (presence of source in municipality and distance to the incinerator) and air dispersion modelling. Environmental multi-media modelling methods were not applied in any of the three groups of studies. CONCLUSIONS: recommendations for refined exposure assessment in epidemiological studies included the use of more sophisticated exposure metrics instead of simple proximity indicators where feasible, as distance from a source results in misclassification of exposure as it ignores key determinants of environmental fate and transport, source characteristics, land use, and human consumption behaviour. More validation studies using personal exposure or human biomonitoring are needed to assess misclassification of exposure. Exposure assessment should take more advantage of the detailed multi-media exposure assessment procedures developed for risk assessment. The use of indicators can be substantially improved by linking definition of zones of exposure to existing knowledge of extent of dispersion. Studies should incorporate more often land use and individual behaviour

Environmentally induced changes in antioxidant phenolic compounds levels in wild plants

[EN] Different adverse environmental conditions cause oxidative stress in plants by generation of reactive oxygen species (ROS). Accordingly, a general response to abiotic stress is the activation of enzymatic and non-enzymatic antioxidant systems. Many phenolic compounds, especially flavonoids, are known antioxidants and efficient ROS scavengers in vitro, but their exact role in plant stress responses in nature is still under debate. The aim of our work is to investigate this role by correlating the degree of environmental stress with phenolic and flavonoid levels in stress-tolerant plants. Total phenolic and antioxidant flavonoid contents were determined in 19 wild species. Meteorological data and plant and soil samples were collected in three successive seasons from four Mediterranean ecosystems: salt marsh, dune, semiarid and gypsum habitats. Changes in phenolic and flavonoid levels were correlated with the environmental conditions of the plants and were found to depend on both the taxonomy and ecology of the investigated species. Despite species-specific differences, principal component analyses of the results established a positive correlation between plant phenolics and several environmental parameters, such as altitude, and those related to water stress: temperature, evapotranspiration, and soil water deficit. The correlation with salt stress was, however, very weak. The joint analysis of all the species showed the lowest phenolic and flavonoid levels in the halophytes from the salt marsh. This finding supports previous data indicating that the halophytes analysed here do not undergo oxidative stress in their natural habitat and therefore do not need to activate antioxidant systems as a defence against salinity.This work has been funded by the Spanish Ministry of Science and Innovation (Project CGL2008-00438/BOS), with contribution from the European Regional Development Fund. Thanks to Dr. Rafael Herrera for critical reading of the manuscript.Bautista, I.; Boscaiu, M.; Lidón, A.; Llinares Palacios, JV.; Lull, C.; Donat-Torres, MP.; Mayoral García-Berlanga, O.... (2016). Environmentally induced changes in antioxidant phenolic compounds levels in wild plants. Acta Physiologiae Plantarum. 38(1):1-15. https://doi.org/10.1007/s11738-015-2025-2S115381Agati G, Biricolti S, Guidi L, Ferrini F, Fini A, Tattini M (2011) The biosynthesis of flavonoids is enhanced similarly by UV radiation and root zone salinity in L. vulgare leaves. 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Association between loop diuretic dose changes and outcomes in chronic heart failure: observations from the ESC-EORP Heart Failure Long-Term Registry

[Abstract] Aims. Guidelines recommend down-titration of loop diuretics (LD) once euvolaemia is achieved. In outpatients with heart failure (HF), we investigated LD dose changes in daily cardiology practice, agreement with guideline recommendations, predictors of successful LD down-titration and association between dose changes and outcomes. Methods and results. We included 8130 HF patients from the ESC-EORP Heart Failure Long-Term Registry. Among patients who had dose decreased, successful decrease was defined as the decrease not followed by death, HF hospitalization, New York Heart Association class deterioration, or subsequent increase in LD dose. Mean age was 66±13 years, 71% men, 62% HF with reduced ejection fraction, 19% HF with mid-range ejection fraction, 19% HF with preserved ejection fraction. Median [interquartile range (IQR)] LD dose was 40 (25–80) mg. LD dose was increased in 16%, decreased in 8.3% and unchanged in 76%. Median (IQR) follow-up was 372 (363–419) days. Diuretic dose increase (vs. no change) was associated with HF death [hazard ratio (HR) 1.53, 95% confidence interval (CI) 1.12–2.08; P = 0.008] and nominally with cardiovascular death (HR 1.25, 95% CI 0.96–1.63; P = 0.103). Decrease of diuretic dose (vs. no change) was associated with nominally lower HF (HR 0.59, 95% CI 0.33–1.07; P = 0.083) and cardiovascular mortality (HR 0.62 95% CI 0.38–1.00; P = 0.052). Among patients who had LD dose decreased, systolic blood pressure [odds ratio (OR) 1.11 per 10 mmHg increase, 95% CI 1.01–1.22; P = 0.032], and absence of (i) sleep apnoea (OR 0.24, 95% CI 0.09–0.69; P = 0.008), (ii) peripheral congestion (OR 0.48, 95% CI 0.29–0.80; P = 0.005), and (iii) moderate/severe mitral regurgitation (OR 0.57, 95% CI 0.37–0.87; P = 0.008) were independently associated with successful decrease. Conclusion. Diuretic dose was unchanged in 76% and decreased in 8.3% of outpatients with chronic HF. LD dose increase was associated with worse outcomes, while the LD dose decrease group showed a trend for better outcomes compared with the no-change group. Higher systolic blood pressure, and absence of (i) sleep apnoea, (ii) peripheral congestion, and (iii) moderate/severe mitral regurgitation were independently associated with successful dose decrease