We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality a...

This paper deals with the assessment of inequality in the distribution of voting power. As voting procedures are modeled as simple games and power evaluated through power indices, two approaches are possible to deal with inequality in this context, depending on whether the power pro ̄les generated by some power index or the simple games that model the voting rules are taken as primitives. In bot...

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of obtained identities, we present new trapezoid-type midpoint-type inequalities convex in context New are by taking advantage convexity property, power mean inequality, Hölder’s inequality. We show that this family generalizes previous research studies special choices. Furt...

This project sets out two broad aims. First, I seek to explain the persistence of racial inequality in an era of formal racial inequality. I offer a theory of power, historically evolved socially embedded power. The theory states that racial inequality is to be explained in the first instance by the way historical racial norms become embedded in practices and processes of path dependent institu...

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability (for an introduction see [9]). The analogue of entropy in the free context was introduced by the second named author in [8]. Here we show that Shannon's entropy power inequality ([6],[1]) has an analogue for the free entropy χ(X...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound...

5 Overview 'Power relations must figure significantly in explanations of poverty and inequality.' This paper examines that statement and concludes that relations of power underpin inequality and are among the critical variables that cause and keep people in poverty. It, therefore, underscores the importance of integrating 'power' into analyses of inequality and poverty. The paper's main objecti...