In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map Λ : Md(C) → Md(C) can be written as the difference between two completely positive maps Λ = Λ1 − Λ2, we propose a possible way to generalize...

We introduce a transport-majorization argument that establishes majorization in the convex order between two densities, based on control of gradient transportation map them. As applications, we give elementary derivations some delicate Fourier analytic inequalities, which turn yield geometric “slicing-inequalities” both continuous and discrete settings. further consequence our investigation pro...

Due to the importance of quantum entangled states in quantum information and computation [1, 2, 3], much effort has been done recently towards an operational characterization of separable states [4, 5, 6]. The manifestations of mixed-state entanglement can be very subtle [7]. Till now there is no general efficient criterion in judging the separability. The Bell inequalities [8], Peres PPT crite...

Abstract In this paper, we generalize a result of Cuttler, Greene, Skandera, and Sra that characterizes the majorization order on Young diagrams in terms nonnegative specializations Schur polynomials. More precisely, introduce generalized notion associated to an arbitrary crystallographic root system $\Phi $ show it admits natural characterization values spherical functions any Riemannian symme...

We investigate geometric and topological properties of $d$-majorization -- a generalization classical majorization to positive weight vectors $d \in \mathbb{R}^n$. In particular, we derive new, simplified characterization which allows us work out halfspace description the corresponding polytopes. That is, write set all are $d$-majorized by some given vector $y \mathbb{R}^n$ as an intersection f...

A pointwise version of the Howard–Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel’s T as well as Kleene/Feferman’s P̂R) is applied to systems of intuitionistic and classical arithmetic (H and Hc) in all finite...

In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using row stochastic (as a special case), define the relation < bdr on c0, which is said majorization. We also obtain some important properties of Pbdr, set all bounded linear operators T : c0 ? c0; preserve Further, it obtained necessary conditions for operator be preserver majorization bdr. Also...