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

David Gross; Martin Kliesch; Richard Kueng; Ulrich Michel

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

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arxiv 1612.07931 v3 pith:APV4X26Z submitted 2016-12-23 cs.IT math.ITquant-ph

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

Ulrich Michel , Martin Kliesch , Richard Kueng , David Gross This is my paper

classification cs.IT math.ITquant-ph

keywords normdiamondboundknownnotenuclearbeencharacterization

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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 note provides a simple characterization of all operators saturating the upper and the lower bound.

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The paper shows that for some pairs of unitary channels, perfect discrimination is possible with separable states but nearly impossible with maximally entangled states, introducing MEWC and MEBC concepts.