Published November 2018
| public
Journal Article
Comments on "Improving Compressed Sensing With the Diamond Norm"–Saturation of the Norm Inequalities Between Diamond and Nuclear Norm
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
- Eprint ID
- 90748
- DOI
- 10.1109/TIT.2018.2861887
- Resolver ID
- CaltechAUTHORS:20181108-092816240
- GSC 260
- Bonn-Cologne Graduate School
- 2015/19/P/ST2/03001
- National Science Centre (Poland)
- 665778
- Marie Curie Fellowship
- ZUK 81
- Deutsche Forschungsgemeinschaft (DFG)
- W911NF-14-1-0098
- Army Research Office (ARO)
- SPP1798
- Deutsche Forschungsgemeinschaft (DFG)
- Created
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2018-11-08Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field