A majorization relation for a sum of two tensor products of positive semidefinite operators

Mohammad A. Alhejji; Cole Kelson-Packer

A majorization relation for a sum of two tensor products of positive semidefinite operators

Rings and Algebras 2026-07-08 v1 Mathematical Physics Combinatorics Quantum Physics

Authors: Mohammad A. Alhejji , Cole Kelson-Packer

Abstract

We use linear programming to prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators. We give an example showing that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.

Keywords

majorization Ky Fan tensor products positive semidefinite operators linear programming

Cite

@article{arxiv.2607.07913,
  title  = {A majorization relation for a sum of two tensor products of positive semidefinite operators},
  author = {Mohammad A. Alhejji and Cole Kelson-Packer},
  journal= {arXiv preprint arXiv:2607.07913},
  year   = {2026}
}

Comments

10 pages, no figures