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

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.

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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.

Item Type:Article
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URLURL TypeDescription
Michel, Ulrich0000-0002-5284-9407
Kliesch, Martin0000-0002-8009-0549
Gross, David0000-0001-8888-3028
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.
Funding AgencyGrant Number
Bonn-Cologne Graduate SchoolGSC 260
National Science Centre (Poland)2015/19/P/ST2/03001
Marie Curie Fellowship665778
Deutsche Forschungsgemeinschaft (DFG)ZUK 81
Army Research Office (ARO)W911NF-14-1-0098
Deutsche Forschungsgemeinschaft (DFG)SPP1798
Issue or Number:11
Record Number:CaltechAUTHORS:20181108-092816240
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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
Deposited By: Tony Diaz
Deposited On:08 Nov 2018 20:47
Last Modified:16 Nov 2021 03:35

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