Note on the saturation of the norm inequalities between diamond and nuclear norm
Information Theory
2018-10-23 v3 math.IT
Quantum Physics
Abstract
The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a regularizer for low-rank matrix recovery. The norm constants that bound the diamond norm in terms of the nuclear norm (also known as trace norm) are explicitly known. This note provides a simple characterization of all operators saturating the upper and the lower bound.
Cite
@article{arxiv.1612.07931,
title = {Note on the saturation of the norm inequalities between diamond and nuclear norm},
author = {Ulrich Michel and Martin Kliesch and Richard Kueng and David Gross},
journal= {arXiv preprint arXiv:1612.07931},
year = {2018}
}
Comments
Simplified proof of the main theorem in [arXiv:1511.01513] and a converse statement. 3+1 pages. V2: small changes and incomplete funding information corrected. V3: minor polishing, published version