$k$-positivity and Schmidt number under orthogonal group symmetries
Quantum Physics
2023-07-21 v2 Mathematical Physics
math.MP
Operator Algebras
Abstract
In this paper, we study -positivity and Schmidt number under standard orthogonal group symmetries. The Schmidt number is a natural quantification of entanglement in quantum information theory. First of all, we exhibit a complete characterization of all orthogonally covariant -positive maps. This generalizes earlier results in [Tom85]. Furthermore, we optimize duality relations between -positivity and Schmidt numbers under compact group symmetries. This new framework enables us to efficiently compute the Schmidt numbers of all orthogonally invariant quantum states.
Keywords
Cite
@article{arxiv.2306.00654,
title = {$k$-positivity and Schmidt number under orthogonal group symmetries},
author = {Sang-Jun Park and Sang-Gyun Youn},
journal= {arXiv preprint arXiv:2306.00654},
year = {2023}
}