Comments on "Improving Compressed Sensing With the Diamond Norm"-Saturation of the Norm Inequalities Between Diamond and Nuclear Norm

Publikationstyp
Review Article
Publikationsdatum
2018-11
Sprache
English
Author
Michel, Ulrich 
Kliesch, Martin 
Kueng, Richard 
Gross, David 
TORE-URI
http://hdl.handle.net/11420/14086
Enthalten in
IEEE transactions on information theory 
Volume
64
Issue
11
Start Page
7443
End Page
7445
Article Number
8424239
Citation
IEEE Transactions on Information Theory 64 (11): 8424239 (2018-11)
Publisher DOI
10.1109/TIT.2018.2861887
Scopus ID
2-s2.0-85050964399
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 paper provides a simple characterization of all operators saturating the upper and lower bounds.