We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any co...

The paper investigates how ex-ante uncertainty about a government policy with redistributive consequences will influence the proportion of agents in favor of it, if agents can trade policy contingent securities. If a subset of agents can insure against policy uncertainty, support for redistributive policies is always smaller than in a case where no insurance is available. Both the relation betw...

Let X , Y be two correlated discrete random variables. We consider an estimation of X from encoded data φ(Y ) of Y by some encoder function φ(Y ). We derive an inequality describing a relation of the correct probability of estimation and the mutual information between X and φ(Y ). This inequality may be useful for the secure analysis of crypto system when we use the success probability of estim...

I report estimates for a fixed-effects model of country-level Gini coefficients as a function of economic freedom along with relevant control variables. Gini coefficients are drawn from the UNU/WIDER World Income Inequality Database Version 2.0a, while economic freedom is measured by the Fraser Institute’s Economic Freedom of the World index. Controls are included for per capita income, politic...

We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, Dür [Phys. Rev. Lett. 87, 230402 (2001)] has shown that there are some multiparticle bound entangled states which are nonseparable and nondistillable, that violate a Bell inequality. We prove that for all the states violating this inequality there exists at least one splitting...

The hypothesis testing problem of two quantum states is treated. We show a new inequality between the error of the first kind and the second kind, which complements the result of Hiai and Petz to establish the quantum version of Stein’s lemma. The inequality is also used to show a bound on the first kind error when the power exponent for the second kind error exceeds the quantum relative entrop...

OBJECTIVES To explore whether the apparent impact of income inequality on health, which has been shown for wealthier nations, is replicated worldwide, and whether the impact varies by age. DESIGN Observational study. SETTING 126 countries of the world for which complete data on income inequality and mortality by age and sex were available around the year 2002 (including 94.4% of world human...

The Brunn-Miknowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual sets. This classical inequality in convex geometry was inspired by issues around the isoperimetric problem and was considered for a long time to belong to geometry, where its significance is widely recognized. However, it is by now clear that the Brunn-Miknowski ineq...

and Applied Analysis 3 Remark 1.5. If f x /x is increasing on I and 1.6 holds, then the Petrović-type functional P1 is nonnegative, that is, inequality 1.4 is valid. Conversely, if f x /x is increasing on I and conditions as in 1.7 are fulfilled, then relation 1.5 holds. In order to define another Petrović-type functional, we cite the following Petrović-type inequality involving a convex functi...