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Note on the saturation of the norm inequalities between diamond and nuclear norm (1612.07931v3)
Published 23 Dec 2016 in cs.IT, math.IT, and quant-ph
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.