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arXiv · 1612.07931

Note on the saturation of the norm inequalities between diamond and nuclear norm

Ulrich Michel·Martin Kliesch·Richard Kueng·David Gross
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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 note provides a simple characterization of all operators saturating the upper and the lower bound.

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Ulrich Michel, Martin Kliesch, Richard Kueng, David Gross. 2016-12-23. Note on the saturation of the norm inequalities between diamond and nuclear norm. https://doi.org/10.1109/tit.2018.2861887

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