Extending a characterization of majorization to infinite dimensions

TL;DR

This paper extends the mathematical framework of majorization and trumping, crucial in quantum entanglement transformations, to infinite-dimensional spaces using advanced tools like Dirichlet series and Riemann-Stieltjes integrals.

Contribution

It generalizes a key majorization result to infinite dimensions, enhancing its applicability in quantum information theory.

Findings

Extended majorization results to infinite-dimensional settings

Linked majorization and trumping with Dirichlet polynomials and Mellin transforms

Provided a mathematical foundation for quantum entanglement transformations in infinite dimensions

Abstract

We consider recent work linking majorization and trumping, two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information, with general Dirichlet polynomials, Mellin transforms, and completely monotone sequences. We extend a basic majorization result to the more physically realistic infinite-dimensional setting through the use of generalized Dirichlet series and Riemann-Stieltjes integrals.