CaltechAUTHORS
Published November 2018 | Version public
Journal Article Metadata-only

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

Creators

  • 1. ROR icon University of Cologne
  • 2. ROR icon University of Gdańsk
  • 3. ROR icon Heinrich Heine University Düsseldorf
  • 4. ROR icon California Institute of Technology
  • 5. ROR icon University of Sydney

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 paper provides a simple characterization of all operators saturating the upper and lower bounds.

Additional Information

© 2018 IEEE. Manuscript received April 10, 2017; revised November 7, 2017; accepted June 9, 2018. Date of publication August 1, 2018; date of current version October 18, 2018. U. Michel was supported by BCGS under Grant GSC 260. M. Kliesch was supported by the National Science Centre, Poland (Polonez 2015/19/P/ST2/03001), within the European Union's Horizon 2020 Research and Innovation Programme through the Marie Skłodowska-Curie Agreement under Grant 665778. R. Kueng and D. Gross were supported in part by the Excellence Initiative of the German Federal and State Governments under Grant ZUK 81, in part by ARO under Contract W911NF-14-1-0098 (Quantum Characterization, Verification, and Validation), and in part by DFG under Grant SPP1798 CoSIP.

Additional details

Identifiers

Eprint ID
90748
DOI
10.1109/TIT.2018.2861887
Resolver ID
CaltechAUTHORS:20181108-092816240

Related works

Describes
10.1109/TIT.2018.2861887 (DOI)

Funding

Bonn-Cologne Graduate School
GSC 260
National Science Centre (Poland)
2015/19/P/ST2/03001
Marie Curie Fellowship
665778
Deutsche Forschungsgemeinschaft (DFG)
ZUK 81
Army Research Office (ARO)
W911NF-14-1-0098
Deutsche Forschungsgemeinschaft (DFG)
SPP1798

Dates

Created
2018-11-08
Created from EPrint's datestamp field
Updated
2021-11-16
Created from EPrint's last_modified field