On symmetric decompositions of positive operators
Functional Analysis
2017-03-23 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry with respect to the Euclidean scalar product and we characterize all such decompositions, comparing our results with the case of SIC--POVMs from Quantum Information Theory. We also generalize some Welch--type inequalities from the literature.
Keywords
Cite
@article{arxiv.1609.05060,
title = {On symmetric decompositions of positive operators},
author = {Maria Anastasia Jivulescu and Ion Nechita and Pasc Gavruta},
journal= {arXiv preprint arXiv:1609.05060},
year = {2017}
}