Michel, Ulrich and Kliesch, Martin and Kueng, Richard and Gross, David (2018) Comments on "Improving Compressed Sensing With the Diamond Norm"–Saturation of the Norm Inequalities Between Diamond and Nuclear Norm. IEEE Transactions on Information Theory, 64 (11). pp. 7443-7445. ISSN 0018-9448. doi:10.1109/TIT.2018.2861887. https://resolver.caltech.edu/CaltechAUTHORS:20181108-092816240
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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.
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| 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. | ||||||||||||||
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| Issue or Number: | 11 | ||||||||||||||
| DOI: | 10.1109/TIT.2018.2861887 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20181108-092816240 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20181108-092816240 | ||||||||||||||
| Official Citation: | U. Michel, M. Kliesch, R. Kueng and D. Gross, "Comments on “Improving Compressed Sensing With the Diamond Norm”–Saturation of the Norm Inequalities Between Diamond and Nuclear Norm," in IEEE Transactions on Information Theory, vol. 64, no. 11, pp. 7443-7445, Nov. 2018. doi: 10.1109/TIT.2018.2861887 | ||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 90748 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||
| Deposited On: | 08 Nov 2018 20:47 | ||||||||||||||
| Last Modified: | 16 Nov 2021 03:35 |
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