Orthogonalization of Positive Operator Valued Measures
Operator Algebras
2022-01-12 v2 Quantum Physics
Abstract
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. Quantitatively, our result are also finer, as we obtain a linear dependance, which is optimal. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra.
Cite
@article{arxiv.2103.14126,
title = {Orthogonalization of Positive Operator Valued Measures},
author = {Mikael de la Salle},
journal= {arXiv preprint arXiv:2103.14126},
year = {2022}
}
Comments
14 pages; v2: improvements in the presentation and small mistakes corrected. To appear in the open access journal Comptes Rendus - Math\'ematique