English

Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix

Quantum Physics 2022-11-21 v2

Abstract

We investigate the set of quantum states that can be shown to be kk-incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices can be shown to have small factor width based only on their eigenvalues). In analogy with the absolute separability problem in quantum resource theory, we call these states "absolutely kk-incoherent", and we derive several necessary and sufficient conditions for membership in this set. We obtain many of our results by making use of recent results concerning hyperbolicity cones associated with elementary symmetric polynomials.

Keywords

Cite

@article{arxiv.2205.05110,
  title  = {Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix},
  author = {Nathaniel Johnston and Shirin Moein and Rajesh Pereira and Sarah Plosker},
  journal= {arXiv preprint arXiv:2205.05110},
  year   = {2022}
}

Comments

21 pages, 2 figures