Extending a characterization of majorization to 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.

arXiv comment8 pages

References in corpus (8)

• Conditions for a class of entanglement transformations
• Entanglement-assisted local manipulation of pure quantum states
• Catalytic Conversion Probabilities for Bipartite Pure States
• Necessary and Sufficient Conditions for the Trumping Relation
• The trumping relation and the structure of the bipartite entangled states
• Catalytic majorization and ${\ell }_p$ norms
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation
• Dirichlet polynomials, Majorization, and Trumping

Cited by in corpus (2)

• Submajorization on ${\ell }^p(I{)}^{+}$ determined by increasable doubly substochastic operators and its linear preservers
• A finite sufficient set of conditions for catalytic majorization