Trumping and Power Majorization

TL;DR

This paper explores the relationship between trumping and power majorization, establishing a Rado's theorem analogue and providing examples to deepen understanding in matrix theory and quantum information.

Contribution

It introduces a novel connection between trumping and power majorization, including a Rado's theorem analogue, advancing theoretical understanding in these areas.

Findings

Established a Rado's theorem analogue for power majorization

Connected trumping relation with power majorization in quantum information

Provided illustrative examples demonstrating the theoretical results

Abstract

Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand, the trumping relation has recently been considered in quantum information, specifically in entanglement theory. We explore the connections between trumping and power majorization. We prove an analogue of Rado's theorem for power majorization and consider a number of examples.